Early Nuclear Fusion Cross-Section Advances 1934–1952 and Comparison to Today’s ENDF Data

Abstract

We describe the advancing knowledge of fusion cross sections from 1934 through the development of the first thermonuclear tests fielded by Los Alamos (the singular entity denoted Los Alamos Laboratory/Los Alamos Scientific Laboratory/Los Alamos National Laboratory at different times is designated “Los Alamos” in this paper) in the Pacific in 1951–1952; this technical history has not been previously documented. We compare these nuclear reaction cross sections to the current state of their knowledge as codified in the Evaluated Nuclear Data File (ENDF) databases, focusing on the Big Five reactions: ³H$(\mathit{d},\mathit{n}{)}^4$He, ³He$(\mathit{d},\mathit{p}{)}^4$He, ²H$(\mathit{d},\mathit{n}{)}^3$He, ²H$(\mathit{d},\mathit{p}{)}^3$H, and ³H$(\mathit{t},2\mathit{n}{)}^4$He. At Oppenheimer’s July 1942 University of California, Berkeley, “galaxy of luminaries” conference, Konopinski suggested that the cross section for ³H$(\mathit{d},\mathit{n}{)}^4$He “DT” could be large, and although Teller described this as an “inspired guess,” we provide evidence instead suggesting that Konopinski knew of a 1938 measurement by Ruhlig that secondary DT reactions were “exceedingly probable.” Bethe’s direction that the DT cross section should be measured at Purdue University (Purdue) in 1943 led to the remarkable and unexpected finding that the DT cross section exceeds deuteron-deuteron (DD) by a factor of 100. This was a game-changing result, making Teller’s dream, i.e., the terrestrial production of fusion energy, feasible. Eyewitness accounts are transcribed from the earliest discoveries of the large magnitude of the resonant DT cross section. A description is given of the Manhattan Project’s early 1942–1944 DD measurements at the University of Chicago, the 1943 DT measurements at Purdue, and the subsequent 1945–1946 DD and DT measurements at Los Alamos. The Los Alamos experiments, led by Bretscher, were the first to extend to very low incident ion center-of-mass energies in the 6- to 50-keV range needed in applications and the first to identify, characterize, and document the 3/2⁺ “Bretscher state” responsible for the resonance-enhanced DT cross section. The early measurements were based on thick-target experiments that required a knowledge of hydrogen-isotope stopping powers, much of which was informed by 1930s German studies. We end with the high-accuracy APSST (named for Arnold, Phillips, Sawyer, Stovall, and Tuck) measurements at Los Alamos, 1951–1952. The very first 1942–1946 measurements were accurate to about 50% or somewhat better, but by the early 1950s, the cross sections were determined much more accurately, to within a few percent of our best values today, which come from R-matrix Energy Dependent Analysis (EDA) code analyses of the data, most notably the very accurate 1980s–1990 Los Alamos DT and DD fusion data from Jarmie and Brown. We show that Fermi, in his 1945 Los Alamos lectures, anticipated the S-factor (for the DT cross section), which is a concept widely used later in nuclear astrophysics. To this long abstract, we add a final tidbit: Marshall Holloway, a coauthor on the first-ever 1943 DT cross-section measurement at Purdue, went on to lead the engineering and fabrication of the first H-bomb test, Ivy Mike.

Keywords:

• Fusion
• thermonuclear cross section
• history

TABLE OF CONTENTS

I. INTRODUCTION

I.A. Notation

I.B. The Big Five TN Reactions

I.C. Outline

II. BACKGROUND: THEORY OF THERMONUCLEAR FUSION REACTIONS

II.A. Gamow Fusion Penetrability

II.B. R-Matrix Approach to Scattering Theory

II.C. Evolving Understanding of the Bretscher 3/2+ ⁵He DT Resonance

II.C.1. Large Resonant Cross Section and Unitarity

II.C.2. Polarization Measurements and Angular Momentum

II.C.3. Modern Understanding

II.C.4. Impact on Elastic Scattering

III. CAMBRIDGE 1934 MEASUREMENTS OF TN REACTIONS

IV. CONTEXT FOR THE SUPER: WORLD WAR II AND THE COLD WAR

IV.A. US First Fusion Considerations and 1942 Berkeley Conference

IV.A.1. DT at the 1942 Berkeley Conference

IV.A.2. Why Might Konopinski Have Guessed a Large DT Cross Section: Experiments?

IV.A.3. Why Might Konopinski Have Guessed a Large DT Cross Section: Theory?

IV.A.4. Oppenheimer’s 1942 Berkeley Summary Memorandum

IV.B. German Fusion Research

IV.C. Soviet Fusion Research

V. DT AND DD CROSS SECTIONS, 1942–52

V.A. Chicago Met Lab, DD, 1942

V.B. Purdue, TD and 3HeD, 1942–43

V.C. Los Alamos, TD and DD, 1943–51

V.C.1. First Handbook of Nuclear Physics, LA-11, 1943

V.C.2. Bretscher’s 1945–46 Experiments

V.C.3. The 1945 Super Handbook

V.C.4. Fermi’s 1945 Lectures

V.C.5. Los Alamos, 1946–50

V.C.6. Tuck’s 1951 TN Data Review

V.C.7. APSST, Los Alamos Advances, 1950s

VI. FUSION REACTION RATES

VII. CONTROLLED FUSION ENERGY CIRCA 1946

VIII. CONCLUSIONS

APPENDIX A. STOPPING POWERS TO INFER CROSS SECTIONS

APPENDIX B. DRAMATIS PERSONAE

B.I. Egon Bretscher

B.II. James Tuck

B.III. Emil Konopinski

B.IV. Edward Teller

B.V. Arthur Ruhlig

APPENDIX C. LOS ALAMOS NUCLEAR PHYSICS CONFERENCE 1946

I. INTRODUCTION

In recent years, there have been breakthroughs in the quest to develop thermonuclear (TN) fusion in the laboratory, notably Lawrence Livermore National Laboratory’s (Livermore’s) inertial controlled fusion laser experiments that reached ignition^[1] and the Culham JET facility’s 2024 record of 69 MJ of fusion energy.^[2] In this context, we review the earliest nuclear science breakthroughs in fusion from 1934 through the early 1950s. Short summaries of the present paper have been published in the American Nuclear Society’s (ANS’s) Nuclear News magazine^[3,4] and on the ArXiv.^[5]

A history of fusion surely must begin 13.8 billion years ago. Since the 1960s, it has been recognized that big bang nucleosynthesis (BBN) formed the light elements through fusion processes. But, less widely appreciated is that the deuterium-tritium D(T,n)α reaction was the source of more than 99% of the ⁴He produced in the big bang,^[4,6,7] which accounts for about 25% (by mass) of the primordial elements created (the remainder being mostly ¹H); see Fig. 1. This helium was one of the sources for triple-alpha production of carbon and subsequently the heavier elements in our universe (the CNO cycle and the proton-proton chain in stars synthesized additional helium). Therefore, a fraction of our human existence can be traced back to the fusion reactions discussed in the present paper.^[4,8]

Fig. 1. A schematic of the dominant BBN pathways and the subsequent triple-alpha carbon formation in stars.^[4] The red curve shows the dominant path, which goes through the DT fusion reaction.

The early history of nuclear physics during the Manhattan Project, 1943–1946, at Los Alamos (Project Y) was presented in a paper that was part of a special issue of the ANS journal Nuclear Technology, following the 75th Anniversary of the Trinity test.^[9] (The singular entity denoted Los Alamos Laboratory/Los Alamos Scientific Laboratory/Los Alamos National Laboratory at different times is designated “Los Alamos” in this paper.) A more extensive set of papers was published in the classified journal Weapons Review Letters,^[10] describing scientific advances required for fission devices. The present paper continues this history, focusing on the parallel effort during Project Y and the years following to develop a fusion device, where TN cross-section advances were needed. Our goal is to present this research for the forthcoming occasion of the 75th anniversary of the seminal Los Alamos experiments that first produced large amounts of terrestrial fusion energy: the Greenhouse George test in 1951, which created substantial DT fusion, and the much larger, 10.4-megaton Ivy Mike test in 1952, which demonstrated a hydrogen bomb.

Our account will be mostly that of American breakthroughs in experimental and theoretical light-nuclear-reaction science, involving key collaborators from Great Britain, together with visionary leadership from immigrants to the United States, namely, Edward Teller, Hans Bethe, and Enrico Fermi. But, like the fission breakthroughs described in our Manhattan Project paper,^[9] the nuclear fusion discoveries first began in Europe, with key advances made in Germany and Britain.

In the case of fission, the 1938 discovery was by Hahn, Meitner, and Strassmann in Berlin. Soon afterward, Frisch and Peierls, working in Birmingham, wrote their (initially) secret memorandum on the feasibility of creating a fission bomb using a critical mass of ²³⁵U, which led to the British “Tube Alloys” atomic war effort and contributed to the subsequent creation of the U.S. Manhattan Project.^[11]

The first insights into fusion came nearly two decades earlier.^[12] In 1920, Aston measured the masses of hydrogen and helium and found a difference between the masses of one helium atom and four hydrogen atoms. Following this, Eddington^[13] at the University of Cambridge (Cambridge) proposed that the source of stellar energy was the fusion of hydrogen into helium. In 1928, Gamow published his paradigm-shifting paper, “Zur Quantentheorie des Atomkernes” (“On the Quantum Theory of the Atomic Nucleus”),^[14] on alpha decay, based on the understanding of quantum tunneling, and then showed that alpha-particle fusion (the inverse process of alpha decay) could be understood using the same formalism.^[15] Atkinson and Houtermans^[16,17] built on Gamow’s work to consider proton fusion processes and showed how these reactions could power the stars.^[18]

The phrase “thermonuclear reactions” was coined by Gamow et al.^[19,20] Soon after this, Cockcroft and Walton built their first accelerator in Cambridge, creating 0.5-MeV protons, and used fusion reactions to split nuclei. By 1932, Cockcroft and Walton had measured ⁷Li(p,α) and compared their results with Gamow’s formula and compared their measured energy release with theoretical predictions based on known nuclear masses. Khriplovich’s fascinating 1992 Physics Today article, “The Eventful Life of Fritz Houtermans,”^[18] describes how the impetus for Cockcroft’s accelerator came from Houtermans’s concept of nuclear fusion reactions.

In 1934, Oliphant et al.^[21] discovered tritium^[22] through accelerator deuteron-deuteron (DD) reactions and measured the substantial fusion energy produced in the ²H$(\mathit{d},\mathit{n}{)}^3$He (or DDn) and ²H$(\mathit{d},\mathit{p}{)}^3$H (or DDp) reactions (see Table I and Sec. IV). In the second half of the 1930s, advances were made on the physics of DD reactions, but progress proved elusive in characterizing tritium and ³He. It was not until 1939 that Alvarez could isolate enough tritium in the University of California, Berkeley (Berkeley) cyclotron, using DD reactions, to determine that it was radioactive.

TABLE I The Big Five Largest TN Reactions and Their Abbreviations for Incident Center-of-Mass Energies Below 1 MeV

Number	Big Five Largest TN Reactions	Reaction Abbreviations	$\mathit{Q}$-Value for Each Reaction (MeV)
1	^2H$(\mathit{d},\mathit{n}{)}^3$He	“DDn”	3.269
2	^2H$(\mathit{d},\mathit{p}{)}^3$H	“DDp”	4.033
3	^3H$(\mathit{d},\mathit{n}{)}^4$He	“DT” or “TD”	17.589
4	^3He$(\mathit{d},\mathit{p}{)}^4$He		18.353
5	^3H$(\mathit{t},2\mathit{n}{)}^4$He		11.332

In 1937, just 2 months before his death, Rutherford wrote a Nature article^[23] on the search for tritium (T), which he called “triterium,” and ³He, beyond their production in accelerator experiments. He summarized the mostly failed attempts to find these isotopes in nature, wondering that since D in water can be measured (after concentration by electrolysis), why cannot tritium also be found? He also described 60- to 70-keV discharge measurements on D gas that should be inducing DD reactions, yet no mass-3 fusion products were found. This led him to make a prescient prediction that the TD and ³HeD transmutation cross sections are large (although his suggestion here was not strongly grounded in the contemporary data). Rutherford concluded, “It may be that the reaction of ³H and ³He with D takes place very easily, so that a stage is soon reached when these isotopes are destroyed in the discharge as fast as they are produced,” and, “The rapid disappearance of ³H and ³He by transmutation would account for the very small abundance of these isotopes in the earth and presumably in the sun.”^a

Rutherford’s 1937 vision “to investigate the interesting transformations that might be expected to occur when the ions of these isotopes [T and ³He] were used for bombarding purposes” would not come to fruition until the first Manhattan Project measurements at Purdue University (Purdue) in 1943 and later at Los Alamos. Then, the remarkable discovery of the large, resonant DT cross section was made (as discussed in this paper). Bretscher’s discovery of the 16.84-MeV $3/2^{+}$ resonance, which we dubbed the “Bretscher state” in his honor,^[4,8] in the A = 5 DT system, at just the right energy needed to enhance the reaction rate, was a game changer in the quest for fusion energy; see Fig. 2. We will also describe (Sec. IV.A.2) a strangely neglected 1938 letter to Physical Review by Ruhlig describing his University of Michigan (Michigan) DD experiment that first reported secondary TD 14-MeV neutrons and pointed to a large TD cross section.^[25] Until we recently highlighted^[3,5] Ruhlig’s letter, its momentous discovery had remained uncited, and its importance had been lost in time (though we argue that it influenced early Manhattan Project fusion research).

Fig. 2. Energy levels in the A = 5 system for the D(T,n)$\mathit{\alpha }$ reaction. Resonant enhancement occurs because the 3/2⁺ energy (16.84 MeV) of the Bretscher state is similar to the D+T separation energy (16.79 MeV).

The present paper focuses on TN fusion cross-section work from 1934 to 1952. We were assisted by the extensive documentation from that period held in the National Security Research Center (NSRC) and library at Los Alamos. The culture of writing scholarly documents on our best “evaluated” understanding of cross sections went back to the Manhattan Project.^[9] The first of these were the Los Alamos nuclear physics handbooks (LA-11, LA-140, and LA-140A). Bethe and Christy were the earliest authors,^[26] and Bethe set high standards in this regard. Subsequent versions were authored by other luminaries, including Victor Weisskopf and Egon Bretscher, the latter of whom had been a British researcher, worked at Los Alamos during the war, and led much TN fusion cross-section work. After the war, in 1947, Robert Wilson, the Los Alamos Physics Division leader, led the writing of a remarkable summing-up of everything that had been accomplished in his extensive “Nuclear Physics,” LA-1009,^[27] which included a chapter on fusion nuclear reactions written by Bretscher and Konopinski, LA-1011.^[28] Later, in 1951, Tuck and Pimbley wrote their valuable LA-1190 review of TN cross sections.^[29] All these papers are available from the Los Alamos library website. Additionally, the U.S. government’s archived letters from the World War II Office of Scientific Research and Development (OSRD),^[30] run by V. Bush and J. Conant, also proved to be invaluable. At the time, the research was shrouded in secrecy; these letters have now been declassified and provide valuable context for understanding the 1940s-era research into fusion.

As these papers reveal, the earliest focus was on pure deuterium as a fuel for TN reactions. In a summary of the Los Alamos “Super Conference,” held from April 18–20, 1946, Bretscher et al. wrote,^[31] “Two general properties of such phenomena were early recognized. First, decisive importance of hydrogen isotopes, especially of the relatively available deuterium. Deuterium provides a fuel for the thermonuclear reaction as uniquely appropriate as is uranium for the fission chain reaction.” Tritium became a feasible isotope to consider only when it could be produced in reactors at Oak Ridge National Laboratory (Oak Ridge) and Hanford, and even then, it was an expensive process that competed with plutonium production. Bretscher went on, “Second, the nature of the physics of this kind of nuclear reaction is qualitatively different from the neutron physics involved in the now familiar fission chain.” Figure 3 shows scientists at the later, August 1946 Nuclear Physics Conference in Los Alamos. See Appendix C.

Fig. 3. A conference at Los Alamos, August 1946. Left to right: The man in uniform, leftmost, is Oliver Haywood. Over his left shoulder is Norman Ramsey. Although we can only see a forehead and some glasses, next to Ramsey is Gregory Breit. Bradbury is up front; next, we have Oppenheimer. Behind Oppenheimer is, perhaps, Herb Lehr. Back on the front row, next to Bradbury, we have John Manley. Over Manley’s shoulder is Feynman. Back to the front row is Fermi. Over Fermi’s shoulder, apparently seated to Feynman’s left, is James Tuck. On the front row all the way over to the right is Jerry Kellogg. According to the inventory, Arthur Schelberg is in the image as well—very likely the half-face behind Feynman. Los Alamos records have this photograph taken around August 1946. The speaker was Philip Morrison; see Appendix C. (Credit: Alan Carr).

Tuck and Pimbley’s LA-1190 review^[29] provides a comprehensive bibliography of relevant work before 1951, beginning in 1930 in Germany (even before Chadwick’s 1932 discovery of the neutron); see Figs. 4 and 5. Their review gives a fascinating account of the experimental challenges they were dealing with to accurately determine cross sections. There is much discussion on topics that might not be expected, for example, hydrogen-isotope stopping powers. This is because in the early days, thick-target yields were measured, from which TN cross sections were inferred. Uncertainties in the stopping powers led to substantial uncertainties in the inferred cross sections. The early 1930s papers from Germany listed in Fig. 4 were on stopping powers and related matters, not on TN cross-section measurements, per se. The 1930 Gerthsen proton range measurements were converted to equivalent projectile deuteron and triton energies and adapted for interpreting the 1934–1946 deuterated thick-target experiments. It was fortuitous that Bethe, the world’s expert in charged-particle stopping powers, came from Germany to the United States and led the Theoretical Division during the Manhattan Project. He was able to provide essential advice on how to determine TN, DD, and TD cross sections from thick-target experiments. This is covered in Appendix A.

Fig. 4. An image from Tuck and Pimbley’s LA-1190 (1951) review paper^[29] showing the bibliography of data related to TN fusion cross sections and stopping powers for deuterium, tritium, and hydrogen (part 1).

Fig. 5. An image from Tuck and Pimbley’s LA-1190 (1951) review paper^[29] showing the bibliography of data related to TN fusion cross sections and stopping powers for deuterium, tritium, and hydrogen (part 2).

Tuck and Pimbley’s LA-1190 bibliography, Figs. 4 and 5, proved invaluable to us in reconstructing the process by which early 1940s work at the University of Chicago (Chicago) and Purdue led to subsequent 1945–1952 measurements at Los Alamos and a postwar expansion of fusion cross-section research at other laboratories and universities.

On the 40th anniversary of the founding of Los Alamos, Dick Taschek provided an interesting perspective^[32] on the early years of the laboratory. When asked about the laboratory’s most important early measurements for TN applications, he said:

The most crucial was the measurement of the cross section for fusing deuterium and tritium. The original idea for a thermonuclear weapon was based on using the energy released in fusing two deuterons [D+D $\to$ ³He+n]. But then tritium was seen at the Berkeley cyclotron in some highly irradiated targets, and Bethe persuaded the Purdue group to measure the DT fusion cross section [D+T $\to$ ⁴He+n]. They accelerated tritium, which probably came out of the accelerator as HT or something like that. Neither Bethe nor anybody else anticipated such a big cross section for the DT reaction. But the Purdue group didn’t have enough energy resolution to really understand their results. Then the work on the DT cross section was transferred to Los Alamos. In 1944 or thereabouts Bretscher and his group measured the DT and DD cross sections again. At that time Los Alamos had the world monopoly on tritium.^b They measured quite a piece of the DT cross section as a function of deuteron energy, and although the energy resolution in the low-energy region of interest was not all that good, they were able to determine that the DT cross section was higher than the DD cross section by a factor of 10 [sic] or more. That was the most important breakthrough for thermonuclear weapons.

This technical history is described in detail in this paper. Also, note that DT is over 100 times larger than DD at the peak of the resonance, and Bretscher’s Los Alamos DD and DT measurements were in 1945, not 1944.

I.A. Notation

We use both notations “DT” and “TD” to describe deuterium-tritium fusion reactions, reserving TD for cases where we want to highlight that the experimentalists used accelerated tritons on a deuterium target (and not the reverse). Since many early measurements used tritons as projectiles, many of our figures present the cross section as a function of triton energy. The results can be easily transformed to the more familiar deuteron projectile laboratory frame using $E_D=2/3E_T$.

We use the notations “DDn” and “DDp” to describe the two branches of the deuterium-deuterium fusion reaction, one creating a neutron and ³He, the other creating a proton and ³H.

I.B. The Big Five TN Reactions

The Big Five reactions, Table I and Fig. 6, are all exothermic (the energy release $\mathit{Q}>0$) reactions that proceed quickly at energies that are typical in environments with temperatures far below 1 MeV ($\simeq$11.6 GK). We are interested in energies for the ions in the range from a few hundred electron-volts to some tens to hundreds of kilo-electron-volts. For example, a controlled fusion reactor is expected to operate with a DT plasma burn in the 10- to 20-keV temperature range, and Livermore’s recent N210808 inertial confinement fusion experiment^[1] created a DT plasma burning at 10 keV.

Fig. 6. The Big Five TN cross sections (in units of barns) versus energy in the c.m. energy frame, from ENDF (upper panel) and associated volumetric reaction rates (sigma-v-bar) versus temperature (lower panel).

Figure 6 shows the cross sections and Maxwellian-averaged rates of the Big Five reactions, named for their importance in TN applications. The notable features are the large 5-b (1 b $\equiv$ ${10}^{-24}$ cm²) peak of the DT cross section owing to the presence of the $3/2^{+}$ resonance and the similar magnitudes of the DDn, DDp, and TT reactions, which are about two orders of magnitude smaller than the DT for energies below 100 keV. The D-³He reaction also shows a resonance owing to the ⁵Li 3/2⁺ state (a mirror of the A = 5 ⁵He state), but its lower-energy fusion cross section is suppressed owing to the larger Coulomb barrier arising from a stronger repulsion, relative to DT, between the deuteron D and the ³He.

For completeness, we show in Fig. 7 the DT and DDn reaction rates at very low temperatures, where interestingly, there is a crossover below 10 eV as the DDn rate becomes larger than that of DT. These results come from the Los Alamos R-matrix Energy Dependent Analysis (EDA) code. Note the roughly 60 log cycles on the figure going from 100 eV down to 1 eV, something rarely seen in evaluated nuclear data calculations! Later, we discuss the reasons why, if the $3/2^{+}$ resonance did not exist, the DD cross section would exceed the DT cross section in the center-of-mass (c.m.) frame; see Sec. IV.A.3. The DT resonance enhances the cross section at energies above $\sim 10$ eV, as previoulsy mentioned, but at the energies less than 10 eV, the system is so far from the resonance peak energy that resonance enhancements are insufficient to overcome the penetrability differences and make the DT larger [see Eq. (12)(12) $\mathit{Penetrability}\left[\frac{\mathit{DD}}{\mathit{DT}}\right]=\mathit{exp}(0.0948/\sqrt{E^{\mathit{cm}}})\mathrm{,}$(12) ].

Fig. 7. The very low-temperature DT and DDn volumetric reaction rates $⟨\mathit{\sigma v}⟩$ (sigma-v-bar) versus temperature (in units of electron-volts) from cross sections determined through the Los Alamos EDA R-matrix code. DT is smaller than DD at the very lowest temperatures, below 10 eV.

I.C. Outline

We begin, in the next section, with an overview of theoretical issues related to fusion reactions of light, charged nuclides. We provide a summary of the theory of charged-particle fusion cross sections, notably Gamow’s penetrability and the astrophysical S-factor, how R-matrix scattering theory is used today to represent these reactions, and we describe the evolving understanding of the important DT 3/2⁺ resonance.

We then describe the first (early 1930s) experimental fusion reaction measurements using Cambridge’s accelerator. These 1934 experiments discovered the large fusion energy release from DD reactions. They also contained within them (although did not draw attention to) information to predict the very large energy release (17.6 MeV) that would come from the DT reaction.

Next, some historical context behind the intense scientific research on fusion is given, for the decade between 1941 and 1952. The United States was in a race to develop nuclear weapons, first against Germany, later against the Soviets. The findings from Oppenheimer’s 1942 Berkeley conference, on the likely feasibility of creating a TN device, are described, together with discussions involving Fermi, Konopinski, Bethe, Teller, Oppenheimer, and others on the potential importance of the DT reaction. We discuss possible experimental and theoretical reasons behind Konopinski’s insight that the DT cross section is large, concluding that it was most likely his knowledge of Ruhlig’s^[25] 1938 Physical Review DT inference from his DD measurement at Michigan.

The major part of the paper then traces the advances in our understanding of DT and DD cross sections through 1952, mostly made for the Manhattan Project, together with follow-on work for the Super hydrogen bomb at Los Alamos. The key cross-section experiments are described: 1942–1943 DD work at Chicago’s Metallurgical Laboratory (Met Lab); 1943 TD measurements at Purdue; 1945–1946 results at Los Alamos for low-energy TD and DDp reactions; and, finally, the high-accuracy Los Alamos APSST measurements for DT and DD from 1951–1952 (named after the Physical Review paper’s authors: Arnold, Phillips, Sawyer, Stovall, and Tuck^[33,34]).

As we trace the evolution of the fusion cross-section measurements from 1934 to 1952, we compare the results against our best modern understanding as embodied in the Evaluated Nuclear Data File (ENDF) database, ENDF/B-VIII.0,^[35] often using ratio plots. We also describe the related evolving understanding of Maxwellian-averaged reaction rates for DT fusion in a hot plasma.

Finally, we briefly discuss some of the earliest thinking on peaceful controlled thermonuclear research at Los Alamos, circa 1946.

Appendix A provides some background on stopping powers used at the time. Appendix B gives short biographical descriptions of some of the leading scientists who worked on the nuclear science of fusion: Bretscher, Tuck, Konopinski, Teller, and Ruhlig. Appendix C briefly describes the 1946 Nuclear Physics Conference at Los Alamos, where Wigner presented his resonance theory. One year later, he published his famous R-matrix resonance formalism with Eisenbud; modern R-matrix results are given in the present paper.

II. BACKGROUND: THEORY OF THERMONUCLEAR FUSION REACTIONS

We view the fusion reaction process in two phases. Two reactant nuclear constituents fuse together (such as D and T), producing a typically short-lived (about ${10}^{-22}$ s) object, i.e., the compound system, formed when all of the constituents of the reactants are closer together than about 1 fm = ${10}^{-15}$ m. In the final stage, the compound system disassociates into two or more product nuclides. In the first phase, the reactants must have sufficient energy to overcome the long-range repulsive Coulomb force exhibited between the like-charged nuclides. And, to create energy in the fusion process, the final products must collectively have less mass than the reactants. The amount of energy generated by the reaction is given by $\mathit{Q}=m_{\mathit{initial}}-m_{\mathit{final}}$; some examples are shown in Table I.

The cross section gives the differential probability that a pair of reactants of a given energy E and quantum state undergo a reaction to a final quantum state with particular energies and angular directions. The scattering and reaction processes are described with the quantum theory via the description of the motion of wave packets of particles, which are determined by solving the Schrödinger equation for the wave function in the presence of appropriate (asymptotic) boundary conditions.^[36] The cross section $\mathit{\sigma }(\mathit{E},{\theta }_{\mathit{CM}})$ (in the c.m. frame) is determined from the wave function as the modulus square of this complex function of the kinematic variables of the reactants and products. In the following section, we describe the quantum theoretic treatment of this ubiquitous problem, originally developed by Gamow.^[14,15]

II.A. Gamow Fusion Penetrability

Following Gamow’s theory of how charged particles can fuse at energies below the Coulomb barrier, theoretical formalisms for understanding the DD and DT cross sections were developed. The 3/2⁺ resonance in the DT channel was discovered during the Manhattan Project and is described further below, where resonance factors in the expression for the angle-integrated cross section augment the Gamow penetrability. We will start, however, by not explicitly accounting for resonances (consistent with the earliest treatments). Many early Los Alamos reports describe the theoretical work on TN cross sections, an example being Teller’s lectures^[37] from the summer of 1951 (see Fig. 8). A slightly generalized form of Teller’s equation, labeled “3.1)” in the excerpt from his notes in the figure, is given as

(1) $\mathit{\sigma }=\mathit{P\pi }{-\lambda }^{2}exp(-2\mathit{\pi }{Z}_1{Z}_2{e}^2/-\mathit{h}\mathit{v}),$(1)

Fig. 8. An extract from Teller’s 1951 Los Alamos lectures on TN physics, LAMS-1450.^[37]

which agrees with Teller’s equation when the charges of the projectile and target, $Z_1$ and $Z_2$, respectively, take on the values $Z_1=1=Z_2$ appropriate for reactants that are isotopes of hydrogen. Here, P, which is discussed in more detail immediately below, was considered by Teller as a sort of “fudge factor,” to take into account effects due to the short-ranged nuclear forces, while v is the relative velocity of the fusing particles. The factor $\mathit{\pi }{ƛ}^2$ is the quantum mechanical geometrical area that the projectile spans, $-\mathit{\lambda }$ being related to the de Broglie wavelength $\mathit{\lambda }$ by $\mathit{ƛ}=\mathit{\lambda }/2\mathit{\pi }=\mathit{\hslash }/\mathit{mv}$, and the exponential factor describes the barrier penetrability. The Coulomb barrier for the DT and DD reactions is near 300 keV (see Sec. IV.A.3) while the energies of concern in TN reactions tend to be in the tens of kilo-electron-volts, which is well below the barrier height. At higher energies, the formula needs to be modified to account for centrifugal barrier effects for higher l partial waves,^[38] but this will not concern us here.

It was recognized that the factor P, which may even have been dependent on the energy $\mathit{E}=\mathit{m}{v}^2/2$, could not be determined with any accuracy from theory available at the time. In LAMS-1450 (1951),^[37] Teller stated, “P cannot be calculated on the basis of our present knowledge and must be determined by comparison with experiment.” It was therefore established empirically by fitting the cross-section data below the Coulomb barrier. They found that for DD reactions, $\mathit{P}\approx 0.3$ (0.15 for each of DDn and DDp), whereas for DT, the probability was approximately 100 times bigger, $\mathit{P}\approx 50$.^[37] Although Teller characterized the factor P as a “reaction probability,” he soon realized that this characterization was too proscriptive since its value for DT had to be assumed to be much larger than unity, which is inappropriate for a probability, which must be in the range (0,1). On the issue of P exceeding unity, and being as large as 50, Teller wrote in 1951^[37] that “since P can’t be a probability, some other part of the formula is incorrect or incomplete, and that the difference is being accumulated into P … due to the resonance.” Just so.

At low energies, one could approximately account for the resonance enhancement by using a larger P value rather than explicitly using a Breit-Wigner–type resonance formula.

The possible energy dependence just mentioned is, in fact, a reality. In the modern, astrophysical formulation, we refine Eq. (1)(1) $\mathit{\sigma }=\mathit{P\pi }{-\lambda }^{2}exp(-2\mathit{\pi }{Z}_1{Z}_2{e}^2/-\mathit{h}\mathit{v}),$(1) by representing the prefactor P to be an energy-dependent S-factor $S_i(E_{\mathit{i},\mathit{cm}})$, giving an equivalent form of Eq. (1)(1) $\mathit{\sigma }=\mathit{P\pi }{-\lambda }^{2}exp(-2\mathit{\pi }{Z}_1{Z}_2{e}^2/-\mathit{h}\mathit{v}),$(1) as^[38,39]

(2) ${\sigma }_i=S_i(E_i^{cm})\frac{1}{E_i^{cm}}\mathit{exp}\left(-\sqrt{E_i^G/E_i^{cm}}\right),$(2)

where $E_i^{cm}$ = c.m. energy of the fusing pair i = DD or DT; $E_i^G$ = Gamow constant $E_i^G=2(\mathit{\pi \alpha }{Z}_1{Z}_2{)}^2{\mu }_i{c}^2=\mathit{f}{\mu }_i$, α being the fine structure constant and ${\mu }_i$ being the reduced mass of the interacting pair with masses $m_{\mathit{i},1}$ and $m_{\mathit{i},2}:$

(3) ${\mu }_i=\frac{{\mathit{m}}_{\mathit{i},1}{m}_{\mathit{i},2}}{m_{\mathit{i},1}+m_{\mathit{i},2}}.$(3)

The reduced masses for DD and DT are, approximately, ${\mu }_{\mathit{DD}}\approx 2\times 2/(2+2)=1\mathit{u}$ and ${\mu }_{\mathit{DT}}\approx 2\times 3/(2+3)=(6/5)\mathit{u}.$ For the pair i = DD or DT, we have, as before, $Z_1$ = 1 = $Z_2$. The reduced wavelength is given by

(4) ${ƛ}^2={\hslash }^2/2{\mu }_i{E}_i^{cm}\mathrm{.}$(4)

In this way of writing the cross section, the factor $S_i(E_{\mathit{i},\mathit{cm}})$ is usually called the “astrophysical S-factor,” an explicitly energy-dependent factor in contrast with the less well-defined and possibly constant factor P. The S-factor accounts for any additional energy dependence, apart from the geometrical factor ${ƛ}^2\sim 1/E_{\mathit{i}\mathrm{,}\mathit{cm}}$ or the exponential Coulomb suppression factor in Eq. (1)(1) $\mathit{\sigma }=\mathit{P\pi }{-\lambda }^{2}exp(-2\mathit{\pi }{Z}_1{Z}_2{e}^2/-\mathit{h}\mathit{v}),$(1) . Thus, S would include the energy dependence that may arise from nuclear resonance effects. (Later, in Sec. IV.A.3, we also discuss how another affect, i.e., that of the outgoing particle final-state phase-space factor, may be included into S-factor considerations, since it varies only slowly with incident energy, compared with incoming particle penetrability effects.)

In Sec. V.C.4, we show that it was Fermi in 1945 who seems to have invented the idea of the S-factor.

II.B. R-Matrix Approach to Scattering Theory

Modern ENDF representations of scattering and reaction data for light nuclei are based on R-matrix evaluations, where measured data are parameterized using numerical code implementations (see below) to preserve essential features of the quantum theory: unitarity and causality. The remarkable progress that was made during the early phases of TN research in the years leading up to 1952 resulted in the important light-element fusion cross sections, i.e., the Big Five, being known to an accuracy of a few percent, independently of the modern, R-matrix approach.

The current ENDF evaluations enjoy the benefit of two innovations, won over time and experience. First, we have much more observational information from experiments on the $\mathit{A}<6$ compound systems than were available in the years leading up to 1952. Further, the types of scattering and reaction information are much more detailed. Whereas in the late 1940s, observations were largely the total-cross-section and angle-integrated cross-section data, we now have information on the angular distribution of the outgoing particles (say, a neutron n and ⁴He nucleus α) from the DT reaction. In addition, we have information about the angular distributions of the outgoing particles that depend on the orientation of how the particles are “spinning” when they interact. This polarization information, the most detailed form of information that describes the collisions of quantum mechanical particles, is highly constraining. When we consider all of this detailed, differential information for all of the processes that couple to a particular compound system, we end up with very little wiggle room in our evaluations.

Let us emphasize this point: We fit all of the processes for a given compound system, say, the ⁵He compound system. These processes are deuteron d elastic scattering, denoted ³H$(\mathit{d},\mathit{d}{)}^3$H; the DT neutron-producing reaction ³H$(\mathit{d},\mathit{n}{)}^4$He; and n elastic scattering ⁴He$(\mathit{n},\mathit{n}{)}^4$He. For each of these scattering and reaction processes, we fit all the different types of data: total, integrated, differential, and polarization. At the end of this procedure, we are, more or less, stuck with a particular cross section (given a sufficiently dense and comprehensive data set). In the case of the light-element TN reactions, this means that despite the 1952 cross sections being very good, we now know that these cross-section values are nearly inevitable, and we know the precision to which all of these detailed data constrain the most important quantities, which are the integrated cross sections. All of this holds because of the realization by Wigner and Eisenbud ^[40] that an important mathematical property of the quantum theory called unitarity, which is a sort of generalization of dispersive physics in classical electromagnetic wave phenomena, could be implemented as a parameterization approach that enforces constraints between different, apparently unrelated, scattering and reaction processes. The resulting unitary theory constitutes the R-matrix approach.

The ENDF/B-VIII.0 (and earlier) evaluated cross-section data come from a series of Los Alamos R-matrix EDA codes (EDA5 and EDAf90, which are collectively referred to as “EDA”). These analysis codes implement a generalized least-squares approach that builds in the physics of unitarity and causality ab initio in order to parameterize, as detailed above, all the available experimental information (often accessed from the EXFOR/CSISRS database^[41]) of measurements from the early days to the present. Some of the most accurate integrated ³H$(\mathit{d},\mathit{n}{)}^4$He cross-section data, ${\sigma }_{\mathit{dt},\mathit{n\alpha }}(\mathit{E}),$ are the Los Alamos Van de Graaff data of Jarmie et al.,^[42,43] Brown et al.,^[44] and Brown and Jarmie,^[45] who measured DT and DD in the 1980s–1990. The EDA code R-matrix evaluations show that not only are these data consistent with ³H$(\mathit{d},\mathit{n}{)}^4$He differential and polarization data but also are consistent with the n and d elastic data. In this way, the EDA R-matrix fits give users a well-determined confidence interval for the cross sections and a built-in quality assurance that the fitted data, independent of theoretical modeling, is a high-fidelity representation of all known observed data.

II.C. Evolving Understanding of the Bretscher 3/2^{+ 5}He DT Resonance

Bethe emphasized the importance of resonances in nuclear physics in his 1937 Reviews of Modern Physics article,^[46] the third part of the “Bethe Bible.”^c By the late 1930s, a ⁵He resonance, accessed by elastic n-α scattering, had been observed^[50,51] at Stanford University (Stanford) and Princeton University (Princeton) for neutrons below 1 MeV. This resonance, however, is caused by the ⁵He $J^{\pi }=3/2^{-}$ ground state^d at a low energy, shown in Fig. 2 as “0 MeV.” This is distinct from the key resonance for the DT reaction [³H$(\mathit{d},\mathit{n}{)}^4$He], i.e., the ⁵He $3/2^{+}$ Bretscher state resonance at an excitation energy of 16.84 MeV (see Figs. 2 and 9). From such early n-α experiments, all that could be inferred was that resonances are possible in these reactions, not that a resonance exists at just the right energy for fusion applications. It was Bretscher and French’s 1945–1946 Manhattan Project experiments^[52,53] to measure the DT cross section [as TD, which is a tritium projectile on a deuterium target, or ²H$(\mathit{t},\mathit{n}{)}^4$He] that definitively discovered and documented the resonance. Subsequent considerations by 1952^[54] correctly assigned it as a $J^{\pi }=3/2^{+}$ state.

Fig. 9. The total cross section for the n+$\mathit{\alpha }$ reaction, showing our EDA R-matrix code’s fit of the measured data. The resonance on the left side of the figure is the A = 5 3/2^– ground state (which was known by 1940). The important 3/2⁺ resonance relevant to the large DT cross section is on the right side, and its identification through 22-MeV neutron experiments would not have been possible in the 1940s.

In the following section, we discuss the character of the 16.84-MeV 3/2^{+ 5}He Bretscher state, of singular importance for the large, resonant cross section in the ³H$(\mathit{d},\mathit{n}{)}^4$He reaction, and sketch the origins of this character in the underlying quantum theory. The assignment of the value of $J^{\pi }$ as $3/2^{+}$ (as opposed to the initially considered value $1/2^{+}$) was ultimately confirmed through the angular distribution of polarized measurements, of which we give a brief account in Sec. II.C.2.

II.C.1. Large Resonant Cross Section and Unitarity

It was evident by the time of the 1945–1946 measurements^[52,55] of Bretscher and French (published in 1949^[53]) that the DT cross section has a large, unexpected resonance at a c.m. energy around 65 keV (equivalent to an excitation energy of 16.84 MeV). The magnitude and importance of this resonance is evident in Fig. 10, where we have used the EDA R-matrix code for a thought experiment to calculate the DT cross section with and without the $3/2^{+}$ state. It is seen that if there was no such state, the DT cross section would be similar to the DD cross section. The importance of this state to fusion technologies and to BBN and anthropic considerations led us to suggest the name “Bretscher state,”^[4,8] in analogy to the “Hoyle state” in carbon that allows for resonant enhancement of triple-alpha nucleosynthesis.

Fig. 10. Cross sections of DT and DD in the incident deuteron projectile laboratory frame, from EDA R-matrix code analyses, including a thought experiment DT calculation in which the A = 5 $3/2^{+}$ Bretscher state is removed.

Early theoretical studies^[56,57] of the DT reaction and its resonance properties led to the consideration that it may have been a $J^{\pi }=1/2^{+}$ resonance (rather than $3/2^{+}$). Though we find flaws in the logic that we surmise from these sources, their reasoning may have been as follows. A schematic representation of the $\mathit{d}+\mathit{t}\to \mathit{n}+\mathit{\alpha }$ reaction is given in Fig. 11 that shows, as we proceed from right to left, three stages of reactions that may be described in terms of the intermediate, compound system. The first stage is the fusion of the deuterium d and tritium $\mathit{t}$ into the ⁵He compound system, $\mathit{dt}{\to }^5$He. The second stage is the formation and evolution of the short-lived, metastable ⁵He system. The final stage is the production mechanism of the final-state $\mathit{n}$ and $\mathit{\alpha }$ particles, ⁵He $\to \mathit{n\alpha }$. At the progression through each stage of the reaction (that is, at the vertices), the $J^{\pi }$ may not change because of the rotational invariance of three-dimensional space. Note, however, that during the transmutation at each vertex, despite the fact that $J^{\pi }$ cannot change, the channel spin s and relative orbital motion $\mathrm{\ell }$ may change in such a way that maintains the $J^{\pi }$. By considering the angular dependence of the products n and α and having knowledge of the spins of the participating reactants and products, the quantum theory allows—though we forego a detailed description here^e —the determination of the possible rotational character, i.e., the $J^{\pi }$, of the transition.

Fig. 11. Schematic of the reaction ³H$(\mathit{d},\mathit{n}{)}^4$He. The diagram is read from right to left, starting with the initial deuterium d and tritium $\mathit{t}$ state (also written $\mathit{d}{+}^3\mathrm{H}$), and moving to the left along the lines labeled d and $\mathit{t}$, their interaction is shown by a shaded, square vertex that represents the transition to the intermediate, short-lived, metastable ⁵He compound system as $\mathit{dt}{\to }^5$He. Continuing to the left from the $\mathit{dt}{\to }^5$He vertex, along the thick, solid black arrow, representing the spatially stationary, time-evolving ⁵He compound system, arrives at a second vertex, which represents the production mechanism ⁵He $\to \mathit{n\alpha }$. The geometric figures indicate spatial symmetry of the incoming (right side) and outgoing (left side) particles (but note that for nonpolarized projectiles, the outgoing particles remain isotropic).

Bretscher’s first fit of the resonant cross-section data used the product of a Breit-Wigner resonance form and the Gamow penetration function [see Eqs. (17)(17) ${\sigma }_{\mathit{DT}}(\mathit{E})=\frac{1}{E}\frac{A}{((E_r-\mathit{E}{)}^2+{\Gamma }^2)}\mathit{exp}(-1.72/\sqrt{(}\mathit{E}))\mathrm{,}$(17) and (20)(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20) later, which are functionally equivalent, but with different numerical constants]. These expressions have the general form

(5) $\begin{array}{c}{\sigma }_{\mathit{DT}}(\mathit{E})=g_J(s_d\mathrm{,}{s}_t)\mathit{\pi }{ƛ}^2\\ \times \frac{{\Gamma }_n{\Gamma }_d}{{(E_R-\mathit{E})}^2+{({\Gamma }_n+{\Gamma }_d)}^2/4}\mathrm{,}\end{array}$(5)

(6) $g_J(s_1,s_2)=\frac{2\mathit{J}+1}{(2s_1+1)(2s_2+1)},$(6)

where $E_R$ = resonance energy; ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Gamma }}_d$ = partial widths in the $\mathit{n}+\mathit{\alpha }$ and $\mathit{d}+\mathit{t}$ channels, respectively; $g_J$ = statistical factor, $\mathit{J}$ = (again) total angular momentum (or simply “total spin”); $s_d$ and $s_t$ = internal spins of the incoming deuterium $s_d=1$ and tritium $s_t=1/2$. In principle, $E_R$, ${\mathrm{\Gamma }}_n$, and ${\mathrm{\Gamma }}_d$ are all energy-dependent quantities, with ${\mathrm{\Gamma }}_d$ changing most rapidly with energy because of the Coulomb barrier. [Equations (17)(17) ${\sigma }_{\mathit{DT}}(\mathit{E})=\frac{1}{E}\frac{A}{((E_r-\mathit{E}{)}^2+{\Gamma }^2)}\mathit{exp}(-1.72/\sqrt{(}\mathit{E}))\mathrm{,}$(17) and (20)(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20) take into account the energy dependence of ${\mathrm{\Gamma }}_d$ in the numerator of the general form but neglect it in the denominator.] The parameters $E_R$ and ${\mathrm{\Gamma }}_n$ are also taken to be constant. Nevertheless, they give a good representation of the cross section near the peak of the resonance. We should mention that Eq. (5)(5) $\begin{array}{c}{\sigma }_{\mathit{DT}}(\mathit{E})=g_J(s_d\mathrm{,}{s}_t)\mathit{\pi }{ƛ}^2\\ \times \frac{{\Gamma }_n{\Gamma }_d}{{(E_R-\mathit{E})}^2+{({\Gamma }_n+{\Gamma }_d)}^2/4}\mathrm{,}\end{array}$(5) is a simplification of the general expression for the cross section, which is appropriate when the cross section is dominated by a single resonance. More generally, the cross section is given by a sum over all possible $J^{\pi }$, with each contribution of the form of Eq. (5)(5) $\begin{array}{c}{\sigma }_{\mathit{DT}}(\mathit{E})=g_J(s_d\mathrm{,}{s}_t)\mathit{\pi }{ƛ}^2\\ \times \frac{{\Gamma }_n{\Gamma }_d}{{(E_R-\mathit{E})}^2+{({\Gamma }_n+{\Gamma }_d)}^2/4}\mathrm{,}\end{array}$(5) .

The measured angular distributions of the outgoing neutron and alpha particles were observed to be very nearly isotropic, and this may have suggested (erroneously) the dominance of the $\mathrm{\ell }=0$ S-wave in the $\mathit{n}+\mathit{\alpha }$ production mechanism.^f If one makes the minimalist assumption that the interactions between nucleons depend only on the distance between them, i.e., a central force model (without complications of so-called spin-orbit or tensor forces, which depend on the spins of the interacting particles), one may expect an outgoing S-wave, too. (We will soon show that that this is not the case; it is in fact an outgoing $\mathit{D}$-wave). Since the outgoing alpha and neutron particle spins are zero and $1/2$, respectively, these spins combine under the rules of the quantum theory to give a unique value of the channel spin s of magnitude $\mathit{s}=1/2$. The channel spin is then combined with the orbital angular momentum (as vectors) to yield the total $\mathit{J}$, $\mathit{J}=\mathrm{\ell }+\mathit{s}$. The observed isotropy suggested the $\mathit{n}$ and $\mathit{\alpha }$ are in an $\mathit{S}$-wave with zero orbital motion $\mathrm{\ell }=0$ and therefore the total $J^{\pi }=1/2^{+}$. Here, the + superscript denotes the parity of the reacting particles, the parity of the ⁵He compound system, and the parity of the products, these all being the same since parity, like $\mathit{J}$, does not change (or is conserved) when traversing the vertices. Parity is useful because the relative orbital motion of two particles has definite values of parity $(-1{)}^{\mathrm{\ell }}$, and its conservation limits the changes in $\mathrm{\ell }$ at each vertex, $\mathrm{\Delta \ell },$ to differ by an even number of units: mod$(\mathrm{\Delta \ell },2)=0$.

If the working assumption that the production of $\mathit{n}$ and $\mathit{\alpha }$ is isotropic with $\mathrm{\ell }=0$ is correct (in fact, it is not correct), then this implies that the ⁵He is uniquely $J^{\pi }=1/2^{+}$; this is often written in nuclear spectroscopic notation as ${ }^2{S}_{1/2}$.^g Given that the $J^{\pi }$ must be maintained at each vertex, and working from left to right in Fig. 11 from the $\mathit{n}+\mathit{\alpha }$ final state to the ⁵He resonance, implies that it, too, must be a $J^{\pi }=1/2^{+}$ resonance state. Then, the incoming d and $\mathit{t}$ must also have $J^{\pi }=1/2^{+}$. Now, however, there is a complication for $\mathit{dt}$ that was not present for $\mathit{n\alpha }$. Whereas only a single value for the channel spin $\mathit{s}=1/2$ is possible for the $\mathit{n}+\mathit{\alpha }$ final state (since the spin of the $\mathit{\alpha }$ is zero, $s_{\alpha }=0$, as we mentioned above), neither of the initial state particles $\mathit{d}$ or $\mathit{t}$ have spin-zero. This implies that the channel spin is not uniquely defined for the $\mathit{dt}$ initial state: It has two possible values. The incoming deuterium $\mathit{d}$ and tritium $\mathit{t}$ spins $s_d=1$ and $s_t=1/2$ combine to give channel spins of either $1/2$ or $3/2$. These channel spins then further combine with an assumed value for the orbital motion of $\mathrm{\ell }=0$—since $\mathit{S}$-waves usually dominate and would seem to be the simplest assumption—to also give $\mathit{J}=1/2^{+}$ or $3/2^{+}$, described in spectroscopic notation as ²S_1/2 and ⁴S_3/2. In this scenario then, assuming that the reaction products $\mathit{n}+\mathit{\alpha }$ are isotropic and with the requirement that the $J^{\pi }$ is conserved throughout each stage of the reaction implies that only a single transition may occur:

(7) $\mathit{dt}{(}^2{S}_{1/2})\to \mathit{n\alpha }{(}^2{S}_{1/2})\mathrm{,}$(7)

and further, as stated previously, this transition must occur through a ⁵He resonant state of the same total $J^{\pi }=1/2^{+}$. Although an application of Ockham’s razor argued for this choice, it was subsequently realized that although (7) represents a transition that was consistent with the requirements of the quantum theory, it was not the transition occurring in nature.

The first indication of a problem with this scenario was that the measured 5-b cross section at the resonance peak exceeded the unitarity limit for a $1/2^{+}$ state. The unitarity limit, which is an upper limit that is a consequence of the quantum theory, is

(8) ${\sigma }_{\text{max}}=g_J\mathit{\pi }{ƛ}^2\mathrm{.}$(8)

Here, $g_J$ is again the statistical factor, defined in Eq. (6)(6) $g_J(s_1,s_2)=\frac{2\mathit{J}+1}{(2s_1+1)(2s_2+1)},$(6) . The theoretical maximum value of ${\sigma }_{\mathit{DT}}$ can occur under a set of conditions that happen to be nearly satisfied by the DT reaction, and it then nearly coincides with the peak of the resonance in Eq. (5)(5) $\begin{array}{c}{\sigma }_{\mathit{DT}}(\mathit{E})=g_J(s_d\mathrm{,}{s}_t)\mathit{\pi }{ƛ}^2\\ \times \frac{{\Gamma }_n{\Gamma }_d}{{(E_R-\mathit{E})}^2+{({\Gamma }_n+{\Gamma }_d)}^2/4}\mathrm{,}\end{array}$(5) , where ${\mathrm{\Gamma }}_n\approx {\mathrm{\Gamma }}_d$. The quantity $\mathit{\pi }{ƛ}^2$ value is 8.3 b at a c.m. $\mathit{dt}$ energy of 65 keV. Then, for a $J^{\pi }$ = 1/2⁺ resonance, the statistical factor $g_{1/2}=2/(2\cdot 3)=1/3$ and the unitarity limit would be (1/3)8.3 b = 2.8 b. The observed cross section of 5 b, however, exceeds this, indicating that (if the unitarity limit is relevant) the statistical factor should be increased. This can be achieved by relaxing the assumption, described above, that the outgoing wave was not $\mathrm{\ell }=0$ but an $\mathrm{\ell }=2$ $\mathit{D}$-wave instead. Such a transition that couples incoming and outgoing waves of different orbital character, such as the $\mathit{s}-\mathit{d}$ transition here, can occur via the well-known tensor component of the nuclear force, which was first identified by Wigner.^[59] In this case, the outgoing channel spin $1/2$ combines with $\mathrm{\ell }=2$ to give total angular momenta and parity of $3/2^{+}$ or $5/2^{+}$, i.e., ${ }^2{D}_{3/2}$ or ${ }^2{D}_{5/2}$. To conserve $\mathit{J}$ (the initial $\mathit{dt}$ particles still come in with $\mathrm{\ell }=0$), the resonance spin must be $3/2$. Thus, we have the transition that actually occurs in nature:

(9) $\mathit{dt}{(}^4{S}_{3/2})\to \mathit{n\alpha }{(}^2{D}_{3/2}).$(9)

Here, the unitarity limit is (2/3)8.3 b = 5.6 b, consistent with the measured value of $\sim$5 b, representing a large fraction of the maximum possible value. The possibility of this transition was recognized in 1951 by Flowers^[57] (see the third equation on p. 505 of Ref.^[57]), but it was thought to be “a priori weaker than the former ones,” including (7). This assumption was likely based on experience with transitions of atomic electrons, which are of a completely different character than nuclear ones.

It was also recognized by Flowers that representations of the cross section over the resonance would require taking into account the energy dependence of ${\mathrm{\Gamma }}_d$ also in the denominator of the expression, and possibly also that of $E_R$. Rather than pursue an explicitly energy-dependent resonance form, however, Flowers chose to parameterize the cross section in terms of a complex scattering length, which is a parameter that describes the nuclear interaction at low energies. He also (correctly) gave arguments that the reaction could be initiated by $\mathit{S}$-waves, contradictory to those given by Konopinski and Teller. By 1951, then, Flowers was close to our modern understanding, but he still thought a $1/2^{+}$ state could be dominant, even though he saw arguments for a $J^{\pi }$ = 3/2⁺ state because of the unitarity limit concerns. It was the Los Alamos paper of Argo et al.^[54] that parameterized the cross section in terms of a single-level R-matrix form with $J^{\pi }=3/2^{+}$. Sometime between Flowers^[57] and Argo et al.,^[54] these researchers correctly settled on the $J^{\pi }=3/2^{+}$ transition as being the dominant one, presumably because the data were described well by a single resonance term, which had to be $\mathit{J}=3/2$ because of the magnitude of the peak cross section.

II.C.2. Polarization Measurements and Angular Momentum

We have just discussed the fairly solid evidence accrued by the 1950s that the Bretscher state is $J^{\pi }=3/2^{+}$. Conclusive evidence of this, however, was not obtained experimentally until the early 1970s.^[60,61] This evidence comes from a class of highly involved and sophisticated nuclear reaction experiments called polarization experiments, wherein one or more of the reactants or products is polarized. These experiments amount to multiple-scattering experiments: The first scattering polarizes, and a second reaction provides the object data sought. In the quantum theory, particles that have nontrivial properties under rotations (i.e., they are not pointlike) can be polarized, i.e., forced to spin along a particular axis, much like light can be polarized by passing it through a polarizing filter or by reflection. Our primary objective in this section is to briefly describe how particle polarization can reveal the angular dependence of the outgoing $\mathit{n}$ and $\mathit{\alpha }$ particles shown schematically on the left side of Fig. 11.

As mentioned above, we now know that the Bretscher excited state in the ⁵He system, which causes a resonant enhancement of the fusion reaction ³H$(\mathit{d},\mathit{n}{)}^4$He, has a spin/parity $J^{\pi }$ = 3/2⁺, dominated almost completely by an initial configuration in the $\mathit{d}+\mathit{t}$ entrance channel with an $\mathit{S}$-wave (or $\mathrm{\ell }=0$) character. This $\mathit{S}$-wave configuration corresponds to that part of the deuterium and tritium system in which these particles have no relative rotational dynamics and are, therefore, isotropically distributed in their c.m. (This is a feature of the wavelike nature of particles in quantum mechanics that confers the possibility of Fourier-resolving any wave into components that have definite properties under rotations.) The outgoing $\mathit{n}+\mathit{\alpha }$ channel, however, is not required to also be a wave of isotropic, $\mathit{S}$-wave character. That this is true is owed to the fact that the neutron $\mathit{n}$ (spin-$1/2$) and the ⁴He nucleus $\mathit{\alpha }$ (spin-$0$) have spins that are different from either the $\mathit{d}$ or $\mathit{t}$. In fact, $\mathit{n}$ and $\mathit{\alpha }$ are observed experimentally to possess a relative orbital motion, and this motion is quantized with two quantum units, or $\mathrm{\ell }=2$. The magnitude of this orbital motion is given by the value $\sqrt{6}\mathit{\hslash }$, where $\mathit{\hslash }\simeq {10}^{-34}$ J∙s is the reduced Planck constant [$\mathit{\hslash }=\mathit{h}/(2\mathit{\pi })$], whose tiny value on everyday, macroscopic scales is characteristic of the quantum theory. [Values of the magnitude of angular momentum are quantized according to ${\ell }^2|\mathit{\ell }\mathrm{,}\mathit{m}〉=|\mathit{\ell }\mathrm{,}\mathit{m}〉\mathit{\ell }(\mathit{\ell }+1){\hslash }^2$, giving for $\mathrm{\ell }=2$, $\mathrm{\ell }(\mathrm{\ell }+1)=6$, whose square root gives the length of the vector $\mathrm{\ell }$; the symbol $|\mathrm{\ell },\mathit{m}⟩$ is a type of complex vector, equivalent in configuration space to the spherical harmonics, $Y_{\ell }^m(\hat{r}\text{)}$.] Such states of two units of orbital angular momentum are called $\mathit{D}$-wave states. The fact that the nuclear interaction can transform an $\mathit{S}$-wave to a $\mathit{D}$-wave implies that it has nontrivial orbital, dynamical properties itself. In fact, this component of the nuclear force with its intrinsic orbital dynamics is the tensor force, which we will discuss in some detail below. Heuristically speaking, the tensor force acts as a dynamo might on the relative orbital motion of the incoming $\mathit{d}+\mathit{t}$ particles. The fact that the initial $\mathit{d}+\mathit{t}$ state is described as a wave of zero relative orbital motion (an $\mathit{S}$-wave) implies that it is therefore spherically symmetric or spinless. (The spherical symbol on the right side of Fig. 11 is indicative of the spherical symmetry of this component of the incoming $\mathit{dt}$ wave.) The tensor force acts on the angular coordinates of the $\mathit{d}+\mathit{t}$, “spinning them up,” before they are converted, through the ⁵He 3/2⁺ resonance, to the final state $\mathit{n}+\mathit{\alpha }$ particles, which are now rotating about one another, as shown schematically on the left side of Fig. 11. This three-lobed shape is the magnitude of the spherical harmonic $|Y_2^0(\hat{r}{)|}^2$ and shows, in particular, that neither the $\mathit{n}$ nor the $\mathit{\alpha }$ can be emitted (in their mutual c.m. frame) at an angle of ${\theta }_{\mathit{CM}}\approx 54.7$ deg with respect to the direction defined by the incoming $\mathit{dt}$ reactants (see Fig. 12).

Fig. 12. Angular dependence (in the c.m.) characteristic of the $\mathit{D}$-wave production of the $\mathit{n\alpha }$ final state in the reaction ³H$(\mathit{d},\mathit{n}{)}^4$He near the peak value of the cross section $E_d=108$ keV. The dashed, zero line intersects the tensor polarization $T_{20}$ at angles $\simeq 54.7$ deg and $\simeq 125.3$ deg with respect to the incident direction; see text. Again, note that for nonpolarized projectiles, the outgoing particles remain isotropic.

How is it, then, that the outgoing $\mathit{D}$-wave for the emitted neutron and alpha particles is observed as isotropic? Isotropy is ensured because the unpolarized angular distribution arises from a summation over the channel spin magnetic quantum numbers. Summing over these magnetic—or directional—quantum numbers effectively removes any dependence on direction arising from the particle intrinsic spins, and since the resonance is formed in the $\mathit{S}$-wave, it may not decay anisotropically as this would imply a preferred direction. There is a general rule for the contribution of a transition matrix element to the differential cross section: The maximum Legendre order it gives is twice the minimum $\mathrm{\ell }$ value of the initial and final angular momentum quantum numbers. So, in this case, the maximum Legendre polynomial that may contribute is $2min(0,2)=0$, and the angular distribution is isotropic. At higher energies (including energies near the resonance), there is some asymmetric forward angular peaking even in the unpolarized differential cross section due to the interference of the $3/2^{+}$ resonance term with other terms, such as $\mathit{dt}{(}^4\mathit{P})\to \mathit{n\alpha }{(}^2\mathit{P})$ transition amplitudes, where the $\mathit{P}$-waves indicate a dipole-like ($cos{\theta }_{\mathit{CM}}$) angular dependence, that begin to become important.

II.C.3. Modern Understanding

The modern R-matrix treatment of the ⁵He and ⁵Li systems^[44,62,63] affords a concurrent fit of nearly 2700 data points, taken by about 35 different experimental setups, with a ${\chi }^2/$degree of freedom $\simeq 1.4$ of experimental data that measured scattering [³H$(\mathit{d},\mathit{d}{)}^3$H, ⁴He$(\mathit{n},\mathit{n}{)}^4$He] and reaction [³H$(\mathit{d},\mathit{n}{)}^4$He, ³H$(\mathit{d},\mathit{n}{ }^{\mathrm{\prime }}{)}^4$He*] processes, where ⁴He* is the first excited state of ⁴He with an excitation energy of 20.2 MeV and $J^{\pi }=0^{+}$. The data include (angle-integrated) cross sections and angular distributions for both unpolarized reactants and products and some angular distributions where some of the participating nuclei (with spin-non-zero) are polarized. This R-matrix approach using the Los Alamos EDA code is the basis for the modern ENDF DT cross-section evaluation, and the present paper shows this ENDF/B-VIII result in many figures, starting with Fig. 6.

The uncertainty in the DT cross section that is obtained from Hale et al.’s ENDF/B-VIII EDA code R-matrix analysis is shown in Fig. 13. The DT fusion cross section is seen to be accurate to a few percent. Just above the peak of the resonance, the unitarity constraint of the S-matrix leads to an uncertainty reduction such that the uncertainty becomes very small, about 0.2%. The ENDF work can be compared to a recent R-matrix analysis by Odell et al.,^[64] which implemented a somewhat complementary approach. Unlike the multichannel EDA matrix, it used one- and two-level R-matrix approximations to examine the data below 210 keV c.m. energy, but it implemented some advanced Bayesian techniques to assess the uncertainties. At 40 keV, the Odell et al. DT result (2.7618 b ± 0.75%) is 1.8% below ENDF (2.8125 b); at 80 keV, the two approaches differ by 0.6%. The results differ slightly not just because of the different methods used but because of different choices regarding which measured data to include. Odell et al.’s work included the 1952 Rice University (Rice) measurement by Conner et al.,^[65] but Hale et al. chose not to include it owing to questions raised by the different shape compared to the other high-accuracy DT measurements.

Fig. 13. The DT fusion cross-section uncertainty (one standard deviation) from the EDA R-matrix analysis for ENDF/B-VIII.

Beyond R-matrix approaches, next, we briefly summarize two other approaches that have been studied recently, one at Los Alamos and the other at Livermore, CEA, and TRIUMF.

At Los Alamos, Brown and Hale^[66] used an effective field theory (EFT) treatment to calculate the ³H$(\mathit{d},\mathit{n}{)}^4$He cross section. This approach introduces a set of mathematical objects called quantum fields, represented as a kind of differential operator (on a Hilbert space, the infinite-dimensional generalization of a vector space), corresponding to stable particles. So, for the D(T,n)α reaction, one has field operators for n, D, T, α, and a stable version of the ⁵He(3/2⁺), which will be affected by its interactions with the other fields to give a particle that resonantly decays into those other stable particles of the theory. Reference^[66] shows that the effect of these interactions upon the stable ⁵He state, described in terms of a mathematical object called the propagator or Green function, is to “dress” the stable ⁵He particle, which causes it to become an unstable, resonant particle. “Dressing” is a consequence of the effect of quantum mechanical fluctuations, which arise from a phenomenon called $\mathit{dt}$ and nα loops. This nomenclature is because in a diagrammatic representation of quantum field theory, developed by Richard Feynman, these fluctuations are represented by closed circles or loops. The reader may have heard the wild statement by Feynman to the effect that, paraphrasing, in the quantum field theory, the particle does anything it likes—it can move in any direction at any speed, moving forward or backward in time. The resulting cross-section formula for ³H$(\mathit{d},\mathit{n}{)}^4$He has three parameters: the two vertex couplings (as in our Fig. 11) and the bare, undressed ⁵He mass. Brown and Hale find a form that is very similar to the Breit-Wigner expression, shown in Eq. (5)(5) $\begin{array}{c}{\sigma }_{\mathit{DT}}(\mathit{E})=g_J(s_d\mathrm{,}{s}_t)\mathit{\pi }{ƛ}^2\\ \times \frac{{\Gamma }_n{\Gamma }_d}{{(E_R-\mathit{E})}^2+{({\Gamma }_n+{\Gamma }_d)}^2/4}\mathrm{,}\end{array}$(5) but with the energy-dependent versions of the widths ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Gamma }}_d$ and the resonance energy $E_R$ explicitly calculated. Their Eq. (18)(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18) displays a Breit-Wigner–like energy denominator: The first term is basically $(\mathit{E}-E_R{)}^2,$ where $\mathit{E}=p_{dt}^2/2m_{\mathit{dt}}$, and the second term is the energy-dependent generalization, mutatis mutandis, of ${\mathrm{\Gamma }}_{tot}^2/4.$

At Livermore, CEA, and TRIUMF, an ab initio no-core shell model with a continuum approach to modeling the DT reaction has been advanced by Hupin et al.^[7] These calculations take, as input, two- and three-body potential interactions, which describe the elemental, basic interaction between nucleons. These potential interactions are derived from a so-called chiral EFT, which possesses some of the symmetries of quantum chromodynamics, the underlying theory of the strong nuclear force. Owing to the complexity of these sorts of calculations, Hupin et al. limited their calculations to the inclusion of a subset of possible clustering of the five nucleons to clusters that describe well-defined deuterons and tritons $\mathit{dt}$ and n⁴He. Their calculations are able to reproduce the resonance energy and cross section to be fairly close to its measured value, which constitutes an impressive result. Distortions of the deuteron appear to play an important role in the calculation of the cross section and its resonant enhancement. Navratil has noted to us that the 3/2⁺ state’s calculated shape properties (the proton and neutron configuration radii) are closer to those of the incoming dt configuration than the n+⁴He configuration. This modern approach^[7,67] builds on the early findings discussed in Sec. II.C.1, in which the transition is dominantly $\mathit{dt}{(}^4{\mathrm{S}}_{3/2})\to \mathit{n\alpha }{(}^2{\mathrm{D}}_{3/2})$, with a tensor force responsible for the transition from an incoming $\mathit{dt}$ $\mathit{S}$-wave to an outgoing $\mathit{n\alpha }$ $\mathit{D}$-wave.

II.C.4. Impact on Elastic Scattering

We note here an interesting prediction that results from the fact that the $J^{\pi }=3/2^{+}$ resonance saturates the unitary limit, as mentioned earlier. This strong resonance is also seen in DT elastic scattering and gives a peak in the nuclear elastic cross section nearly as large as in the reaction cross section, albeit at a different energy. This is shown in Fig. 14 by a calculation from the Los Alamos R-matrix analysis of the ⁵He system, which gives the elastic cross section (not including the Coulomb interaction contribution) and, for comparison, the reaction cross section over the same energy range. The behavior of both cross sections can be understood qualitatively in terms of the single-level expression in Eq. (6)(6) $g_J(s_1,s_2)=\frac{2\mathit{J}+1}{(2s_1+1)(2s_2+1)},$(6) . The reaction cross section in that expression is maximized when ${\mathrm{\Gamma }}_d={\mathrm{\Gamma }}_n$ at the resonance energy $E_R$. A similar expression to give the behavior of the nuclear part of the elastic cross section has ${\mathrm{\Gamma }}_d^2$ in the numerator of the resonance term instead of ${\mathrm{\Gamma }}_n{\mathrm{\Gamma }}_d$. However, when the two widths become equal, the elastic and reaction cross sections are the same, and that accounts for the similar behavior of the cross sections over the resonance in this case, Fig. 14. Differences in the energy dependence of the two cross sections occur due to the different power of the strongly energy-dependent width ${\mathrm{\Gamma }}_d$ in the numerator of the resonance term.

Fig. 14. The integrated nuclear cross sections (in units of barns) for the DT reactions, at c.m. energies between 0.01 and 4 MeV, as calculated from the Los Alamos R-matrix analysis of the ⁵He system. The solid red curve is for elastic scattering, and the dashed blue curve is for the D(T,n)α reaction.

Modern R-matrix evaluations (performed using the Los Alamos R-matrix analysis code EDA) correctly account for the effect of the $3/2+$ resonance in the DT elastic differential cross section. Recently, we found a previously neglected low-energy measurement by Balashko and Barit^[68] from 1958 that, while of low accuracy, indicates the importance of the nuclear interaction contribution in the ratio in Fig. 15. There, the differential cross section was measured at $90$ deg in the laboratory frame, and the figure shows a graph of the quantity $\mathit{\sigma }/{\sigma }_R$, the ratio of the DT differential cross section to that of the differential cross section for Rutherford scattering.

Fig. 15. The ratio of the elastic DT differential scattering cross section $\mathit{\sigma }$ over the differential cross section for Rutherford scattering ${\sigma }_R$ at $90$ deg computed from the Los Alamos EDA R-matrix evaluation^[44] and plotted with data from Balashko and Barit.^[68]

We first note that while Ref.^[68] is unclear as to whether they are plotting the differential cross section $\mathit{\sigma }$ relative to the Rutherford cross section ${\sigma }_R$ in either the laboratory or c.m. frames, it is immaterial—the transformation factor cancels in the ratio. Here ${\sigma }_R$, the Rutherford cross section, is the differential cross section for two structureless point particles that interact only by the (repulsive) Coulomb interaction and no other forces (such as those that arise from the strong nuclear force). While the detailed shape of $\mathit{\sigma }/{\sigma }_R$ does not compare accurately to the data of Balashko and Barit, the systematics are reproduced. That is, at low energies, in the region of the $3/2^{+}$ resonance, there is a dip in the ratio due to a destructive-interference effect between the contribution of the resonance to the DT scattering and that of the Coulomb interaction. The fact that the energy at which the minimum occurs in Fig. 15 coincides roughly with the peak of the ${\sigma }_{\mathit{elas}}$ curve in Fig. 14 is a good indication of the importance of the $3/2^{+}$ resonance in understanding this effect. At energies above the resonance energy, the ratio is essentially linear according to both the R-matrix evaluation and the data, although the slope differs. We tend to believe that the R-matrix evaluation is the more accurate representation given that the modern evaluation (represented by the data in the ENDF/B-VIII.0 file) depends on all of the scattering and reaction data and utilizes both unpolarized and polarization information.

Now that we have provided an overview of fusion reaction theory, we next proceed to describe historical fusion cross-section advances from 1934 on.

III. CAMBRIDGE 1934 MEASUREMENTS OF TN REACTIONS

The first laboratory measurements of TN fusion energy were made in Cambridge’s Cavendish Laboratory, 1933–1934. In Ref.^[21], Oliphant, Harteck, and Rutherford measured the probability for deuterium fusion (DD fusion) to create both possible low-energy reactions: proton and triton (pT) and neutron and ³He (n³He) products with deuterons that were accelerated to several hundred kilo-electron-volts. Harteck is acknowledged for preparing the heavy water target; later, he would work on the World War II German atomic bomb project, while Oliphant would contribute to the Allied radar effort and Manhattan Project. The Cambridge experiment measured the large kinetic energy of the secondary particles: “We were therefore surprised to find that on bombarding heavy hydrogen with diplons [their name for deuterons] an enormous effect was produced.”^[21] They also identified the isotope tritium for the first time.^[22] The importance of these papers, which herald the discovery of nuclear fusion, certainly rival the papers that first reported the discovery of fission that came half a decade later (see Ref. [9]).

During these heady early days of exploring $\mathit{E}=\mathit{m}{c}^2$, Oliphant et al. accurately measured the positive exothermic $\mathit{Q}$-value of 4.0 MeV that is produced for the D(D,p)T reaction (our best value today is 4.03 MeV), as well as the $\mathit{Q}$-value for D(D,$\mathit{n}$)³He of 2.5 to 3.6 MeV (our best value today is 3.3 MeV). They also correctly determined that these two branches of the DD reactions are of similar magnitude. Their approach was as follows.

First, for the D(D,p)T reaction, they observed the secondary particles with their ranges of 1.6 cm (for tritons) and 14.3 cm (for protons), respectively, in various media. They knew from calibrated range relationships that the latter could be ascribed to protons with an energy of 3 MeV. The other particle of mass-3 moved in the opposite direction and, from momentum conservation, had to be ~1 MeV (neglecting the small incident energy of the deuterons). Thus, they determined the $\mathit{Q}$-value to be 4 MeV, a very large energy. Then, the authors determined the triton mass. Their mass-energy conversion corresponded to a mass unit of 1 u = 925 MeV, which is different from the modern value of the Dalton (1 u ≈ 931.494 MeV) and obtained by averaging four cases in the paper where they provide examples of this conversion^[21]). In their mass units, a helium nucleus is 4.0022-u mass units, and the proton is 1.0078 u (measured earlier by Aston^[69]). The deuteron mass was taken as 2.01363 u from Bainbridge’s 1933 Philadelphia’s Franklin Institute mass spectrometry measurements.^[70] From this, they could conclude from the D(D,p)T reaction that the triton’s mass is ($2\times 2.01363)-1.0078-4$ MeV/925 MeV = 3.0151 u. The authors then provided supporting evidence that the measured range of the tritons, 1.6 cm, is consistent with the hypothesis that they were observing the D(D,p)T reaction (realizing that slowing-down ionizations from tritons should be the same as for protons of the same velocity).

Next, the D(D,n)³He reaction was described. Evidence was presented to suggest that the secondary neutrons, measured through recoil reactions, were comparable in number to the proton secondary particles from the D(D,p)T branch. (Consistent with this, modern ENDF/B-VIII.0 evaluations of DDn and DDp cross sections differ by no more than ~10% below DD c.m. energies of 50 keV.) They estimated the energy of the neutrons to be about 2 MeV (versus ~2.5 MeV assessed today) and could only infer the presence of ³He recoils but not observe them directly owing to their lower energy. But, from a separate study of the p+⁶Li reaction creating ³He and ⁴He, they inferred the ³He mass to be 3.0166 u, again taking advantage of Bainbridge’s mass for ⁶Li. From these arguments, they assessed the $\mathit{Q}$-value for D(D,n)³He to be in the range 2.5 to 3.6 MeV (our value today is 3.3 MeV).

Since this experiment determined masses for the triton and ³He, one could then easily determine the $\mathit{Q}$-values for other important TN reactions. Using the above triton T mass from Oliphant et al., together with the D mass from Bainbridge and well-known n and α masses, one would derive a D(T,n)α reaction $\mathit{Q}$-value of $2.01363+3.0151-1.0067-4.0022$ = 0.01983 u, or 18.3 MeV, close to the modern value of 17.6 MeV. Although this could have been done, it was not explicitly stated in 1934. The importance of the large $\mathit{Q}$-value for the DT reaction was certainly known later in the 1930s^[25] and at the July 1942 Berkeley “galaxy of luminaries”^h conference, where the feasibility of a hydrogen bomb was discussed; earlier evidence regarding its large cross section includes Rutherford’s 1937 Nature paper^[23] and the 1938 Physical Review paper by Ruhlig,^[25] which we describe later in Sec. IV.A.2. But, it would not be until 1943 that sufficient tritium could be produced at Berkeley to measure the TD cross section (at Purdue; see Sec. V.B).

With hindsight, we can reflect that in this 1934 Cambridge experiment, not only was the DD fusion energy release very large, but also it was even larger than that found from fission on a per-nucleon basis. The prompt energy released in fission is ~$0.76$ MeV/nucleon compared to ~$0.91$ MeV/nucleon in DD fusion. In fact, the energy released in DT fusion is about four times (!) larger than that released in fission, per unit mass.

III.A. DD Cross Section

In their seminal paper,^[21] Oliphant et al. did not quote an inferred DD cross section, but there are sufficient experimental details provided in their paper to infer the value. It seems likely that these researchers, or others soon after, would have done so. To extract a cross section from the measured DDp thick-target production rate, one has to assume a stopping power for the projectile deuterons in the deuterated compound target and also to know details such as the solid angle subtended by the proton detector. Stopping powers today are not known to much better than 20% at energies around 100 keV, and in those days, they were yet more uncertain. Nevertheless, Lestone^[72] has assessed what DDp cross section can be inferred from Oliphant et al.’s paper and finds a DDp cross section within a factor of 2 of our best values today (28 mb versus ENDF’s 15 mb, at 100-keV deuteron energy), which is quite remarkable for the first-ever measurement in 1934. We show later, in Sec. V.A, that by 1942–1944, the Chicago Met Lab measurements were accurate to 20% of today’s values.

IV. CONTEXT FOR THE SUPER: WORLD WAR II AND THE COLD WAR

The Cold War with the USSR drove the race to develop the hydrogen bomb (the Super), but it is less well known that there were concerns in the early 1940s that Germany could be attempting to develop TN weapons, in addition to atomic weapons. In this section, we briefly survey the U.S. advances from 1941 on and then summarize related work in Germany and in Russia. Here, we provide only a brief overview, with an eye to cross-section work described later in the paper.

IV.A. U.S. First Fusion Considerations and 1942 Berkeley Conference

In the fall of 1941, at Columbia University, Fermi suggested to Teller that it could be possible to use a fission bomb to ignite TN deuterium fuel.^[73] Initial considerations by Teller indicated that X-ray emission would render the idea untenable, but later, more thorough calculations by Teller and Konopinski were more encouraging. In July 1942, Oppenheimer held a small conference at Berkeley’s Le Conte Hall; he referred to this conference^[71] using the term “galaxy of luminaries.” It included some of the leading physicists of the day to assess the feasibility of developing a fission bomb.ⁱ The following theorists were in attendance: Oppenheimer, Bethe, Konopinski, van Vleck, Bloch, Frankel, Nelson, Serber, and Teller. These scientists quickly concluded that a fission bomb could be developed, in agreement with earlier studies by Britain’s MAUD Committee^[75] [an almost complete version of “Report by M.A.U.D. Committee on the Use of Uranium for a Bomb”^[75] (missing only Appendix 5) made its way to the U.S. National Archives and is online at http://ipfmlibrary.org/maud.pdf] and the U.S. National Academy of Science.^[76] At Teller’s instigations, despite Oppenheimer’s attempts to bring the focus back to a practical weapon based on fission, much of the Berkeley meeting was devoted to whether a Super could be built, at least in principle.^[77]

We can speculate regarding the manifold considerations driving the project at this early stage. As nuclear astrophysicists, the complex science involving thermonuclear reactions, hot plasmas, and radiation transport held a natural interest and fascination for them. Additionally, in Oppenheimer’s “multiple approaches” way of thinking about risk mitigation in the development of a “practical, military weapon,”^[71,78] deuterium, being relatively easy to make compared to other materials with its high energy density relative to ²³⁵U or ²³⁹Pu, may have been attractive as a source of nuclear fuel, complementing the very-difficult-to-produce fissile actinides.

In any event, the group came to the firm conclusion that the Super could be produced. In his August 20, 1942, summary^[79,80] of the meeting, described in more detail in Sec. IV.A.4, Oppenheimer wrote (with surprising optimism) that “We have reached the conclusion that there is one method that can be guaranteed to work, and we wish here to report briefly our findings.”

Bethe summarized this meeting memorably in his obituary of Oppenheimer^[77]:

Teller, Oppenheimer and I, indulged ourselves in a far-off project—namely, the question of whether and how an atomic bomb could be used to trigger an H-bomb. Grim as the subject was, it was a most exciting enterprise. We were forever inventing new tricks, finding ways to calculate, and rejecting most of the tricks on the basis of the calculations. Now I could see at first-hand the tremendous intellectual power of Oppenheimer who was the unquestioned leader of our group. The ideas we had about triggering an H-bomb later turned out to be all wrong, but the intellectual experience was unforgettable.

The Berkeley conclusion had a swift impact. Within a month, on September 18, 1942, Compton, of Chicago’s Met Lab, wrote to James Conant^[30,74] about “Oppenheimer’s new result,” saying the following:

We have already the best advice available in the country from the strictly theoretical physicists. What is needed next is an assessment of their conclusions by a group of men who combine theoretical and experimental physics and are well familiar with the field. It is the three men, Fermi, Wigner, and Allison that I have chosen as most competent representatives of this aspect of physics … for I should rely more strongly upon the practical judgment of the problems involved than I should on the judgment of the theoretical physicists who are responsible for its development to the present stage.

Compton was not convinced that theoreticians were the right people to trust regarding the practicability of developing a hydrogen bomb!

From a security perspective, these remarkable conclusions, from the Berkeley meeting, caused some panic in Washington regarding the perceived lax security controls. The new ideas on the Super were spreading fast, beyond authorized personnel. Starting around September 1, 1942, the OSRD (Wensel, for Bush, e.g., to Lawrence and to Urey^[30]) initiated a campaign to identify all people who had heard of the new Super ideas and shut down information flow, even asking that the people involved “do not let the information go any further, and if possible erase it from their memories.”^[30] Compton made an initial request to Conant on September 1 to brief Fermi, Allison, and Wigner on “Oppenheimer’s new idea” (the Super). It was initially denied but subsequently approved on September 28. Fermi et al., however, were cautioned to employ extreme secrecy regarding the “thermal nuclear reactions” topic and were told that the information was not yet “available to representatives of the army, the engineers, or our British allies.”^[30]

In fact, after this flurry of H-bomb activity in the fall of 1942, Oppenheimer insisted that the Manhattan Project focus almost exclusively on the matter at hand: the development of atomic weapons to help end the war, in the race against Germany. Nevertheless, Oppenheimer did list the TN fusion topic among the nine focus areas he itemized for standing up the new Los Alamos laboratory (see Carr’s Fig. 2 in Ref. [81], item H: “What are the chances of initiating thermonuclear reactions?”), and he authorized Teller to lead a small group to continue thinking about the Super. During the 1943–1946 period, designs were evolved for the Classical Super, building on the ideas sketched out in 1942 at Berkeley^j and set down in a series of Los Alamos reports and patents with authors that included Teller, Oppenheimer, Fermi, Bethe, Konopinski, von Neumann, Fuchs, and Bretscher.^k As described below, TN fusion cross sections were measured at Los Alamos during this Manhattan Project period.

IV.A.1. DT at the 1942 Berkeley Conference

The first insight that T$(\mathit{d},\mathit{n}{)}^4$He (DT) would be an advantageous reaction for fusion, occurring at a lower temperature than either D$(\mathit{d},\mathit{p})$ or D$(\mathit{d},\mathit{n})$ (together DD), was by Emil Konopinski at Oppenheimer’s July 1942 Berkeley conference, which preceded the Manhattan Project. In his 1955 Science article, “The Work of Many People,”^[83] Teller said, “I remember particularly the suggestion of Konopinski that the reactions of tritium should be investigated. At that time it was a mere guess. But it turned out to be an inspired one.” Konopinski’s idea is also reported briefly in Teller’s Memoirs (Ref. [73], p. 172). This is a case where Teller’s memory is not quite correct. It was not a “mere guess,” for it is likely that Konopinski had either read the 1938 Physical Review and remembered a short paper by Ruhlig^[25] (see Sec. IV.A.2) or had heard of Ruhlig’s work. (Konopinski and Ruhlig were both at Michigan during the time frame 1933–1936.) He likely knew of Rutherford’s suggestion in 1937 in Nature.^[23]

The Los Alamos NSRC archives contain a 1986 oral history interview with Konopinski^[84]; Ref. [84] provides an audio clip that we extracted. Finding the key statement on tritium was somewhat fortuitous—by MBC—for the first interview tape revealed nothing, and it was only toward the end of the second tape, 1 h and 8 min in, that the interviewer raised the tritium question. When asked to describe his suggestion to use tritium, Konopinski replied:

That was way back in Berkeley…. I happened to know from pre-war work that the reaction of deuterium with hydrogen-3 produces much more energy and has a larger cross section than D+D. I knew also that ³H could be produced in tiny amounts wherever there were neutrons, namely the reactors that Fermi and company were building. When they produce plutonium they produce a lot of ³H besides; tritium it’s called. I just happened to remember these things from my pre-war things…. We had these continuous conversations going on about rates of reactions. I happened to know this rate of reaction was a very good one, a very rapid one, but the material was very unobtainable. ²H, heavy water, is available in huge quantities. Ocean has a lot of it. But hydrogen-3 has to be produced painfully. But I was thinking of it only as a sort of salting of the deuterium, to help things along, to boost, to make it easier to ignite….

I remember it concretely came to me while we were on our way from a restaurant, back from where we had lunch, going back to business. As soon as I thought of that I whispered it to Hans Bethe and he thought it was a good idea, and the first thing we got back was he told everybody.

Below, we will explore possible reasons for Konopinski’s suggestion that the DT cross section would be advantageous, whether based on experiments that had been conducted prior to 1942 (Sec. IV.A.2) or based on known nuclear theory understanding from the time (Sec. IV.A.3). We will conclude that the situation is exactly as Konopinski recalled in his 1986 interview, i.e., that he most likely knew this from “pre-war work” (experimental work, in fact, by Ruhlig^[25] at Michigan in 1938) and from suggestions in Rutherford’s 1937 Nature paper.^[23]

However, we have found no evidence of a direct measurement of the DT cross section prior to the 1942 Berkeley meeting. Ruhlig’s brief 1938 report of his Michigan experiment, described below, was indirect and involved only circumstantial evidence for the (now known) large, resonant DT fusion reaction.

While as early as 1934,^[21] the masses of deuterium and tritium were known with sufficient accuracy to appreciate the large $\mathit{Q}$-value for T$(\mathit{d},\mathit{n}{)}^4$He (about 18 MeV), which is significantly larger than D$(\mathit{d},\mathit{n})$ or D$(\mathit{d},\mathit{p})$ at roughly 3.3 and 4.0 MeV, respectively—see Sec. III—the DT cross section would have been far less certain. It is the case, though, that measurements of DD reactions^[21,85–87] predate declarations of war by both the United States in December 1941 and Britain in September 1939.^l

We are confident that the DT reaction cross section was not directly measured before the 1943 work of Baker and Holloway at Purdue, described below in Sec. V.B. This Purdue experiment was commissioned by Bethe for the Manhattan Project. Data were obtained in August and published a few weeks later in September 1943 (in LAMS-11^[89]), over a year after the Berkeley conference. Reasons for our confidence that the Purdue experiment was the first direct DT measurement are the following:

1. Bretscher and Konopinski’s comprehensive 1947 review, “The Reactions of Very Light Nuclei with Deuterons in the Low Energy Region,” LA-1011,^[28] states (p. 1), “Baker, Holloway, King and Schreiber made the first observations of the reactions T + D … and 3He + D.”

2. The summary of the 1943 Purdue cyclotron experiments by Purdue historians,^[90] together with one of the key original authors (Schreiber), makes it clear these were the first TD “discovery” experiments; see Sec. V.B. They state that “Dr. Hans Bethe was in frequent communication with us about these measurements and for a time he simply did not believe our results” (because their measured DT cross section was so very high—a surprise). The 1943 LAMS-11 Purdue publication^[89] did not cite any earlier measurements.

3. We consider it unlikely that any other country’s effort, outside of the Manhattan Project, had the necessary combination of technical ability, resources, and will to produce enough tritium for the DT cross-section experiment before Oppenheimer and Manley prioritized it in late 1942; see Sec. IV.A.4. Nuclear reactor breakthroughs, which eventually became a source of tritium via ⁶Li$(\mathit{n},\mathit{t})$ reactions, became feasible only after Fermi’s pile went critical in December 1942. Using a cyclotron to produce tritium via the D on a heavy water target reaction required a heroic effort at Berkeley in 1942–1943. Indeed, on February 1, 1943, Holloway wrote to Dr. Martin Kamen^[91] at Berkeley, politely complaining that the tritiated heavy water sample provided was woefully short of tritium atoms: “The beam we can reasonably expect from this sample may be so small that we will have to sacrifice some accuracy in the measurements. Bethe is reluctant for us to have to do this.” Holloway said that they were told by Bethe and Oppenheimer that they would get a sample having a T/D ratio of ${10}^{-6}$ but received only ${10}^{-8}$. The reply from Berkeley stated that the sample received “was the best he had and could make.” Holloway decided they had no choice but to proceed with the sample on hand (a good decision!).

IV.A.1.a. Manley 1942 Planning Documents from Chicago

In 1942, John Manley was working at Chicago’s Met Lab where he helped manage cross-section work at universities across the United States while also undertaking his own cross-section measurements (DD reactions). During the Berkeley conference, on July 25, 1942, Oppenheimer wrote to Manley on his new interest in the DT cross section.^[92] His request is worth quoting in full:

There is one other experiment which we have just got to get done. It is a lulu! We want to know the cross section for the reaction of ³H with D and the two lithium isotopes. We have about a microgram of this material in 10g of heavy water and Lawrence suggested that we could get rid of the DH beam using the longer range of the ³H energy of the cyclotron. Now I have a complicated proposal which comes from Bethe, although he would not like Gibbs at Cornell to know that. It is this. There is a good cyclotron at Harvard where the beam can be brought out. At Cornell there are two men, Baker and Holloway, who have had a lot experience with the tricky detection work. Our recommendation is that these men and others to assist them, perhaps Livingood and Livingston, be sent to Harvard to operate the cyclotron there, which can carry out, among other things, these experiments with ³H. I want to add a word of caution about this experiment. If our ordinary conversations are secret, this should be secret squared; that is, we should like to have knowledge of our interest in this subject restricted to the absolute minimum and if possible not to have it appear to having connection with our tubealloy project.… Also, we should like to know the cross section for the reaction ⁶Li($\mathit{n}$,³H) for neutrons in the range of 100 or so kilovolts.

Note not only the urgency to measure the DT cross section but also the early (1942) appreciation of the value of ⁶Li($\mathit{n}$,³H) reactions for fusion.

Following the Berkeley meeting, Compton arranged a conference in Chicago on September 21, at which Oppenheimer, van Vleck, Bethe, Teller, and Manley were present. Manley’s summary document, “Notes on CF Conference, Week of September 21, 1942,”^[93] reveals a dramatic increase in attention to the role of light fusion cross sections, versus an earlier June document that focused on fission.^m That document rather surprisingly begins Sec. II.1 with “Mass 3 Experiments,” which is surprising just because fission bomb priorities, surely the highest priority, were described later in items II.2 through II.10; see Fig. 16.

Fig. 16. An extract from John Manley’s work plan following the Chicago CF Conference, week of September 21, 1942.^[93] Note that in the plan shown here, the intention was to measure DT (“Mass 3”) at Harvard or Princeton. In fact, Baker and Holloway were transferred from Cornell to do the measurement at Purdue’s cyclotron, after which they moved to Los Alamos. (We are not sure what “CF” stood for here, but documents from that period had a numbering system involving “C” where “C” stood for “Chicago”; perhaps “F” represented a fission compartment).

Two proposals for these tritium experiments were identified, one for a measurement at Harvard University (Harvard) with van Vleck as official investigator and the other at Princeton with Smyth as official investigator, Fig. 16. In both cases, the possibility of Baker and Holloway, from Cornell University (Cornell), joining the experiment was noted, with a decision to be made by Bethe et al. at a September 27 meeting in Ithaca. As a reflection of its importance, “McMillan to assume active responsibility for the experiment” was stated (McMillan being the future Nobel Prize winner). For reasons outlined in a progress report to Compton on April 30, 1943,^[30] an alternative choice was subsequently made: Baker and Holloway were to do the experiment using Purdue’s cyclotron. This was based on the suitability of the Purdue cyclotron, the availability of two experienced local physicists (King and Schreiber), and the proximity to Chicago.^[30] On October 12, 1942, Oppenheimer wrote^[30] to Holloway, “It seems to me that the arrangements at Purdue are likely to work out very well and I am glad that at long last this subject has found a home.” In those days, the phrase “at long last” could be used for the period between Bethe proposing the experiment in July 1942 and October 1942! See Sec. V.B for details on this seminal first-ever DT cross-section measurement at Purdue.

The same Manley document identified a priority: “11. Manufacture of H³ from Li⁶(n,$\mathit{\alpha }$)H³ by exp. pile proposal” (Fig. 17), that is, the production of tritium through insertion of ⁶Li into a pile using an approach that remains the standard way of making tritium. It is noteworthy that this tritium production path was identified before Fermi’s reactor had achieved criticality, in the same way that plutonium production was planned! The Purdue DT cross-section experiment would use tritium supplied by Segrè from the Berkeley cyclotron that used deuterons incident on a heavy water target.

Fig. 17. An extract from John Manley’s work plan following the Chicago CF Conference, week of September 21, 1942.^[93] The handwritten edits by Manley include a last item, 11, noting that tritium should be made in a pile (reactor). See Fig. 16 for an earlier extract from this plan.

The document also appears to consider what kinds of “small scale devices” could be produced to prove out the feasibility of fission and fusion processes. It is not clear what was meant by this but perhaps is a laboratory-scale demonstration experiment to prove the feasibility of explosive processes. The first set of listings refers to fission processes, but then a separate listing is given for TN processes to study, including the reactions DDn, DDp, DT, D-³He, and n-d scattering, as well as reactions involving neutrons on boron, lithium, and beryllium isotopes.

Clearly, by late 1942, fusion processes had evolved from being a particular interest of Teller’s to becoming a research program planned for the broader U.S. nuclear community.

We next discuss what might have been behind Konopinski’s 1942 suggestion of the benefits to using DT fusion, first from experimental evidence and then from theoretical considerations.

IV.A.2. Why Might Konopinski Have Guessed a Large DT Cross Section: Experiments?

IV.A.2.a. Ruhlig’s 1938 Physical Review Letter

Our (MWP) detailed search of the prewar literature, spanning the years from 1934, when tritium was discovered,^[21] to the 1943 DT measurement,^[89] turned up a 1938 experimental paper^[25] on the likelihood of deuterium and tritium reacting to produce neutrons and ⁴He, together with Rutherford’s 1937 suggestion^[23] (described further below). This time frame was selected following the comment by Konopinski^[84] in the 1986 interview regarding his recollection of “pre-war” knowledge that the DT rate was larger than DD (see Sec. IV.A.1). Arthur Ruhlig’s letter to the editor in the August 1938 issue of Physical Review is the single reference found that provided a quantitative assessment, describing work done in close proximity to, if not part of, his thesis work,^[94] which was completed in 1938. The main focus of the work detailed in Ruhlig’s letter, titled “Search for Gamma-Rays from the Deuteron-Deuteron Reaction,” was the “discovery” reported earlier that year by T. W. Bonner at Rice that the reaction of 0.11-MeV deuterons on heavy phosphoric acid (D₃PO₄) yields excited states of ³He in the reaction ²H$(\mathit{d},\mathit{n})$³He*. (Our current understanding holds that there are no proper resonant states of ³He; Ref. [95] finds virtual bound states, however.) Ruhlig studied the DDn reaction using 0.5-MeV deuterons on a heavy phosphoric acid target, using a high-voltage ion-tube accelerator. Not having found a significant gamma-ray signal corresponding to Bonner’s putative 2-MeV ³He excitation (“not more than one gamma-ray for every 200 neutrons”), Ruhlig makes his momentous comments:

During the course of this investigation many protons were observed which penetrated a carbon sheet $0.15$ cm thick, and consequently had an energy greater than 15 MeV. Since these were present when the chamber was separated from the target by 4 cm of lead, they must be due to neutrons, possibly from the secondary reaction

${ }^3\mathrm{H}{+}^2\mathrm{H}{\to }^4\mathrm{He}+\mathrm{n}+17.6\mathrm{MeV}(2)$

due to recoiling ³H nuclei from the reaction

${\hspace{0.17em}}_{\hspace{0.17em}}^2\mathrm{H}+{\hspace{0.17em}}_{\hspace{0.17em}}^2\mathrm{H}\to {\hspace{0.17em}}_{\hspace{0.17em}}^3\mathrm{H}+{\hspace{0.17em}}_{\hspace{0.17em}}^1\mathrm{H}.(3)$

We understand that energetic protons from the analogous reaction of ³He with ²H have been reported by Oliphant [cites Bethe, unpublished]. The ratio of the number of these very energetic recoil protons to those of the 2.6 MeV group was of the order of one to one thousand; consequently reaction (2) must be an exceedingly probable one. [Italic type our emphasis.]

(In fact, Oliphant^[96] later retracted his measurement quoted above, owing to his discovery of boron contamination, presumably the ³He + ¹⁰B $\to$ ¹²C + n reaction, with the high-energy neutrons producing high-energy recoil protons.)

It seems likely that Ruhlig was thinking that he observed secondary reaction of tritons on deuterium. The chain of events would have been as follows. Roughly 1-MeV tritons are born with high velocity from the reaction of the 0.5-MeV beam deuterons [$\mathit{d}(0.5\mathrm{MeV})$] interacting with the deuterons in the heavy (deuterated) phosphoric acid target through D[$\mathit{d}(0.5\mathrm{MeV}),\mathit{p}$]T(1 MeV) reactions. These tritons then cause secondary TD reactions on the deuterium in the acid as they are slowed in the acid target; see Fig. 18. These secondary TD reactions produce high-energy neutrons with energies above 15 MeV. Ruhlig’s documentation is minimal, but he provides a key useful measured quantity described above as being “one to one thousand.” This ratio is proportional to the ratio of high-energy neutrons produced by D${\left(\mathit{t}(1\mathrm{MeV}),n(14\mathrm{MeV})\right)}^4$He to those of low-energy, 2.6-MeV neutrons produced in D$(\mathit{d}(0.5\mathrm{MeV},\mathit{n}(2.6\mathrm{MeV}){)}^3$He. Since the DDn and DDp branches are roughly equal, Ruhlig’s experimental data are suggesting (roughly) that for every 1000 tritons born in DDp reactions with a few-mega-electron-volt energy, one of them had undergone a secondary DT fusion reaction. As we discuss next, this may be too many DT reactions based on our current understanding of stopping powers.

Fig. 18. Illustration of in-flight reactions where the DD fusion creates a moving triton that then induces a DT fusion, first documented by Ruhlig in 1938.^[25]

This observation can be compared quantitatively to our theoretical understanding today based on DT cross sections and triton stopping powers in phosphoric acid. Our Los Alamos colleagues Lestone et al.^[97] have calculated what we think Ruhlig should have observed regarding the secondary in-flight DT reactions following DD reactions in his experiment. The results suggest that Ruhlig should have observed secondary fusion DT reactions at a much smaller rate than he reported, perhaps three to four orders of magnitude smaller. Lestone et al. calculate the number of in-flight TD reactions for a triton born at 1.1 MeV as 4.8 $\times$ 10^–5 ± 20% (confirmed by a separate FLAG simulation by Stephen Andrews; we also thank George Zimmerman for an independent Livermore calculation that gave a similar result, 3.6 $\times$ 10^–5). To compare to Ruhlig’s recoil proton ratio, this is reduced by the relative efficiencies of n-p recoil detection for DTn versus DDn, together with the requirement that the DTn n-p proton recoils exceed the 15-MeV threshold to penetrate Ruhlig’s 0.15-cm carbon sheet. With varying plausible assumptions of what exactly was observed for the lower- and the higher-energy recoils, the calculated ratio can vary substantially. But, Ruhlig did produce some DT neutrons: When he placed a 4-cm piece of lead between the target and the detector (shielding all protons), he still saw larger than 15-MeV proton events from the DT neutron n-p recoils.

Lestone et al.^[97] are considering another scenario, permitted by the scant description in Ref. [25] that may explain the higher 1:1000 ratio observed by Ruhlig. It is possible that most of the detected high-energy protons did not come from neutron-induced proton recoils but instead came from the parallel process D(D,³He)n followed by ³He(D,p)$\mathit{\alpha }$, aided by their direct proton detection without the need for an intervening n-p scattering in the cellophane foil. (This scenario though, is only possible if Ruhlig’s “one to one thousand” observation occurred in a measurement configuration where the 4 cm of lead was not present; see Ref. [97].)

It is also plausible that Ruhlig was instead observing DT reactions where secondary tritons that had stopped in the target built up over time, during the course of the experiment or in earlier experimental runs, and then underwent DT fusion reactions with beam deuterons. To quantify this probability, one needs to know information that is not now available, i.e., his beam current, spot size, and length of irradiation. If one chooses sufficiently optimistic values for these parameters, one can reachⁿ Ruhlig’s “one to one thousand” reported value for DT neutrons compared with DDn neutrons. A firm conclusion regarding the processes observed by Ruhlig is hampered by a lack of detail in his short 1938 paper.

This Ruhlig paper^[25] is the earliest quantitative reference that we have found to the rate and, therefore, indirectly, the cross section of the DT reaction (except for Rutherford’s 1937 paper,^[23] which is yet more indirect and not quantitative).

Note that Ref. [5] in Ruhlig’s paper^[25] reads as follows: “Unpublished; private communication from H. A. Bethe.” This footnote establishes a link between Ruhlig, perhaps through his thesis advisor H. Richard Crane, and Bethe. It is at least plausible then that Konopinski, who was on a National Research Council fellowship at Cornell under the supervision of Bethe at the time, would have been privy to this finding. Also, we think it probable that Konopinski and Ruhlig knew each other: They were contemporaries at Michigan in the early 1930s; Uhlenbeck was Konopinski’s thesis advisor and was also acknowledged in Ruhlig’s thesis. As a young talented researcher, Konopinski likely read Physical Review diligently! We wonder if at the time of Ruhlig’s publication, his results were considered flimsy given that his paper has been cited so minimally and never before cited for its “exceedingly probable” DT suggestion. This line of speculation is at least consistent with what we take as the suggestion on Konopinski’s part—rather than a declaration—that tritium had potentially advantageous properties concerning its reaction rate with deuterium.

Independent of our calculations and assessments of what might have occurred in Ruhlig’s 1938 experiment, the point still stands that he had suggested DT reactions be exceedingly probable in the peer review literature that Konopinski most likely read.

A related piece of evidence that Konopinski had known Ruhlig’s paper is that Ruhlig talks about DT as a “secondary reaction” and it is exactly such secondary DT reactions that Oppenheimer focused on in his August 20, 1942, memorandum summarizing the Berkeley meeting, described in Sec. IV.A.4 below. The suggestion of the importance of secondary reactions has also been credited to Bethe at the Berkeley meeting.^[88]

It is also very likely that Konopinski and others at the Berkeley conference knew of Rutherford’s 1937 Nature paper,^[23] which also suggested a high DT rate. It was an insightful suggestion, but the evidence supporting it was indirect. Furthermore, recent calculations by our colleague Cameron Bates do not support the arguments (and as we have said, direct DT cross-section measurements could not be done until sufficient tritium was produced in 1943).

We first reported the 1938 Ruhlig DT observation in the April 2023 ANS Nuclear News,^[3] before which Ruhlig’s strangely neglected paper had been cited only seven times—and only between 1938 and 1945—and never for its secondary DT fusion insight. It seems to have been quickly forgotten. In recent years, the National Ignition Facility (NIF) has used such secondary in-flight DT neutron production in DD capsules to study plasma stopping powers.^[99,100]

IV.A.2.b. n-α Scattering

Konopinski et al. would have been well aware of earlier, 1939–1940, measurements that showed a resonance in n-$\mathit{\alpha }$ scattering, by Staub and Tatel (Stanford)^[50] and by Barschall and Kanner (Princeton).^[51] However, the n-$\mathit{\alpha }$ system resonance observed for neutron energies of about 1 MeV was sensitive to the ground state 3/2^– resonance in the A = 5 system, which has nothing to do with the 16.8-MeV $\mathit{D}$-wave 3/2⁺ resonance seen in the DT channel; see Fig. 2. An n-$\mathit{\alpha }$ scattering experiment sensitive to this key 3/2⁺ resonance would be possible using only 22.15-MeV neutrons (4/5 $\times$ 22.15 = 17.72 MeV c.m. energy relative to the n+$\mathit{\alpha }$ mass and about 110 keV above the D+T threshold), and such high-energy neutron sources were not available at that time^o ; see Fig. 9. The 1942 Berkeley conference participants would have known, therefore, that these n-$\mathit{\alpha }$ 1-MeV neutron resonance measurements could not be used to predict a large and resonant DT cross section. Thus, this seems unlikely to be an explanation.

IV.A.2.c. ³He+D Fusion Reactions

If this cross section (Fig. 6. upper panel, red curve) had been measured and the large resonance enhancement seen, presumably it could have been said that charge symmetry would argue for a similar resonant enhancement in TD. However, we do not think that the ³HeD cross section was directly measured prior to the 1943 Purdue experiment (done just before they measured T+D) reported in LAMS-2.^[101] Bretscher and Konopinski, in LA-1011,^[28] explicitly state that Purdue was the first. Also, the aforementioned Oliphant 1938 paper^[96] (with retraction) says he had not observed this reaction by 1938. The Purdue ³He+D measurement did in fact observe a relatively large fusion cross section (0.8 b at 0.65 MeV, 0.5 b at 1.0 MeV), but we find no documentation of the scientists commenting that it is large, or hypothesizing a resonance, let alone also concluding there should be a an isobaric analog mirror resonance in the TD system, too. Today, we know that the ⁵He system produced in DT has a 3/2⁺ resonance at 16.84 MeV above the ground state whereas the ⁵Li system produced in ³HeD has an analog 3/2⁺ resonance at 16.87 MeV above its ground state. Given that the ³He laboratory energy for this resonance is 629 keV, the Purdue measurement at 650 keV did probe this resonance region. But, this line of argument seems not to have been pursued.

Lestone et al.^[97] have identified another potential missed opportunity. In our discussion of Ruhlig’s 1938 experiment, we noted the possibility that Ruhlig had observed D(D,³He)n followed by ³He(D,p)α. If more work had been done in 1938 to clarify this, then the ³He(D,p)$\mathit{\alpha }$ fusion cross section could have been estimated. This would have revealed a large resonance enhancement, which could have pointed (through knowledge of isobaric analog physics) to a large resonance-enhanced DT fusion cross section.^[97]

In summary, then, from an experimental perspective, the only compelling evidence that could have sparked Konopinski’s 1942 Berkeley DT insight appears to be Ruhlig’s 1938 experiment described in Sec. IV.A.2.a.

IV.A.3. Why Might Konopinski Have Guessed a Large DT Cross Section: Theory?

We now know that the DT cross section is enhanced because of the 16.76-MeV 3/2⁺ resonance in the A = 5 system (Fig. 2). While modern ab initio many-body calculations using realistic nucleon-nucleon forces provide insights into the resonance and its energy,^[7] this physics was not known in 1942. This section explores some other theoretical physics, which were known by 1942, that could have been considered by Konopinski. We will conclude that no theory of the time would have sparked the idea of a large DT cross section.

IV.A.3.a. Phase Space

Could the larger $\mathit{Q}$-value for DT imply a larger phase space for the ejectiles, according to Fermi’s Golden Rule,^p and, therefore, a larger DT cross section relative to DD? As we have noted, the large 17.6-MeV $\mathit{Q}$-value would have been known in 1942 since it could be inferred from measurements of masses back in 1934 (Sec. III). Also, from a basic physics perspective, it would have been recognized that having an extra neutron in the initial state (i.e., D+T instead of D+D) would produce a more tightly bound isotope of helium in the final state and, thus, give a larger $\mathit{Q}$-value for the reaction. Early cross-section expressions would usually lump the final state phase space into a constant (the S-factor or equivalent) since it changes so slowly compared with the incident projectile penetrability energy dependence. The outgoing phase-space factor goes as the outgoing momentum $\mathit{k}$ [$\mathrm{i}.\mathrm{e}.,$ $\sqrt{(}\mathit{E})$], as, for example, published by Wigner and Eisenbud in their 1947 R-matrix theory paper for their final state penetrability in what could be considered as an S-factor. Comparing D(T,n)α versus D(D,n)³He, the $\mathit{Q}$-values are 17.6 MeV versus 3.2 MeV, so the phase-space enhancement ratio would be $\sqrt{17.6/3.2}$ = 2.3. Thus, one might expect a DT versus DDn enhancement of a factor of about 2 based on phase-space effects, which is not particularly large.

IV.A.3.b. Coulomb Barrier Differences for DT and DD

What else might have been considered? Might it have been thought that the tritium nuclear radius is larger than the deuteron radius (it actually is not), so that when the fusing nuclei touch, the peak of the Coulomb repulsion occurs at a larger distance so that the DT barrier is lower?

If the interaction radius where the nuclear force sets in is $R_i$ in units of fermi, then the Coulomb barrier is

(10) $U_B=1.44\left[\frac{Z_1.Z_2}{R_i}\right]\mathrm{MeV}.$(10)

If one used general systematics for nuclear sizes, the formula for the interaction radius has been used,^[39] $R_i=1.4(A_1^{1/3}+A_2^{1/3})$ fm, suggesting $R_i^{DD}=3.52$ fm and $R_i^{DT}=3.78$ fm. Putting these numbers into the above equations gives Coulomb barriers of $U_B^{DD}\approx 410$ keV, $U_B^{DT}\approx 380$ MeV, and $U_B^{D^3\mathit{He}}\approx 760$ MeV.

Thus, the above logic might have led to the thought that the DT cross section would be somewhat larger than DD because the Coulomb potential barrier to penetrate is (just a little) lower. But, there are two problems with this argument. The first problem is that in reality, the deuteron is less tightly bound per nucleon than the triton, leading to the deuteron having the larger radius. Modern estimates of the deuteron and triton radii are 2.128 and 1.755 fm, respectively.^q Because the nuclear interaction extends roughly 1 fm beyond such radii, we estimate the Coulomb barrier peaks at nuclear interaction radii, for DT and DD, of 4.9 fm and 5.3 fm, respectively.^r This leads to Coulomb barriers $U_B^{DT}\approx 294$ keV and $U_B^{DD}\approx 272$ keV, with the DT barrier being actually a little higher.

The second problem to note is that the Coulomb barrier $U_B$ does not actually feature in the simple Gamow equation used at the time, Eq. (1)(1) $\mathit{\sigma }=\mathit{P\pi }{-\lambda }^{2}exp(-2\mathit{\pi }{Z}_1{Z}_2{e}^2/-\mathit{h}\mathit{v}),$(1) . As Teller notes in his lectures—see the bottom of Fig. 8—the fact that the penetration occurs only to the radius of the nuclear potential well and not to radius zero leads to only a small correction to the Gamow exponent, especially for incident energies well below the barrier height. In a more rigorous treatment, the differences in nuclear interaction radii are taken into account in the S-factor, not the Gamow penetrability factor. In an R-matrix treatment, on the other hand, the penetrability depends on both the energy and the nuclear radius, so they are not separated as in the S-factor form, and the penetrabilities for D+D and D+T are somewhat different at the same incident deuteron energy.

But, in any case, the DT Coulomb barrier is higher than the DD barrier because the triton nuclear radius is actually lower than the deuteron nuclear radius, though this might not have been known in the early 1940s.

IV.A.3.c. DT and DD Penetrability Compared, If There Were No DT Resonance

It is interesting to ask whether one would expect the DD or DT cross section to be larger if there were no DT resonance enhancement effects. This is because we have wondered what the 1942 Berkeley conference attendees thought on this given they did not yet know of the key 16.84-MeV 3/2⁺ DT Bretscher resonance.

The answer will depend upon whether one asks if it is for the same c.m. energy or the same incident laboratory energy. Here, we will start by assuming that the question is for the same incident laboratory deuteron energy, incident on a D or a T target. We will consider the case where the S-factor differences between DD and DT can be ignored. For a projectile A on a target B, the available c.m. energy $E_i^{cm}$ can be obtained from $E_A^{lab}=E_i^{cm}.(m_A+m_B)/m_B$. Using Eq. (2)(2) ${\sigma }_i=S_i(E_i^{cm})\frac{1}{E_i^{cm}}\mathit{exp}\left(-\sqrt{E_i^G/E_i^{cm}}\right),$(2) , we will consider the Gamow penetrability ratio for DD and DT:

(11) $\begin{array}{rl}& \mathit{Penetrability}\left[\frac{\mathit{DD}}{\mathit{DT}}\right]\\ & =\frac{exp(-\sqrt{E_{DD}^G/E_{DD}^{cm}})}{exp(-\sqrt{E_{DT}^G/E_{DT}^{cm}})},\\ & =\frac{exp\left(-\sqrt{f/(E_D^{lab}/2)}\right)}{exp\left(-\sqrt{(\mathit{f}\cdot 6/5)/(E_D^{lab}\cdot 3/5})\right)}=1& (11)\end{array}$(11)

where $\mathit{f}$ is defined below Eq. (2)(2) ${\sigma }_i=S_i(E_i^{cm})\frac{1}{E_i^{cm}}\mathit{exp}\left(-\sqrt{E_i^G/E_i^{cm}}\right),$(2) but cancels out. Thus, we find that for the same incident laboratory deuteron energies, we expect the Gamow penetrability of the DD and DT reactions to be identical.

If we instead ask about the penetrability DD and DT differences for the same c.m. energy, then in Eq. (2)(2) ${\sigma }_i=S_i(E_i^{cm})\frac{1}{E_i^{cm}}\mathit{exp}\left(-\sqrt{E_i^G/E_i^{cm}}\right),$(2) the differences between DT and DD just come from the reduced-mass differences in the exponential (negative, in the numerator). Since the reduced mass is smaller for DD, the penetrability for DD is actually larger than DT by the ratio

(12) $\mathit{Penetrability}\left[\frac{\mathit{DD}}{\mathit{DT}}\right]=\mathit{exp}(0.0948/\sqrt{E^{\mathit{cm}}})\mathrm{,}$(12)

where $E^{\mathit{cm}}$ is in units of mega-electron-volts. At 100 keV, DD is larger by a factor 1.35, and at 1 keV, it is larger by a factor of 20.

The question is what one should make of the geometrical wavelength factor $\mathit{\pi }{\lambda }^2$ differences. The DD-to-DT ratio is

(13) $\begin{array}{rl}& \frac{\pi {\lambda }_{DD}^2}{\mathit{\pi }{\lambda }_{DT}^2}=\frac{{\mathit{\mu }}_{\mathit{DT}}{E}_{DT}^{cm}}{{\mu }_{\mathit{DD}}{E}_{DD}^{cm}},\\ & =\frac{(6/5)\cdot (3/5)E_D^{lab}}{1\cdot (1/2)\cdot E_D^{lab}}=36/25,& (13)\end{array}$(13)

indicating that for the same laboratory deuteron energy, the DD cross section would be larger than the DT cross section. Two factors are in play here: (1) the smaller DD reduced mass means that its wavelength is larger (more quantum, less classical) and (2) the kinetics implies that for a given laboratory energy, the c.m. energy is smaller for DD, which also results in a larger wavelength for DD.

In conclusion, there is no increase of DT compared with DD when considering only Gamow penetrability and projectile wavelength $\mathit{\pi }{\lambda }^2$ effects. Indeed, the DT cross section would be smaller than the DD if there were no resonance in the DT case. This was also seen earlier in Fig. 7 for reaction rates at very low energies, where the resonance effects are less influential.

As a thought experiment, we can compare our R-matrix calculations of the DD cross section with the DT cross section when we remove the $3/2^{+}$ 16.76-keV resonance from the A = 5 compound system. Using the Los Alamos EDA code, which provides the basis for the ENDF DT and DD evaluations, we obtained the results previously shown in Fig. 10. The result obtained is that without the resonance, the DT cross section is smaller than DD. This is qualitatively consistent with the simple arguments given above.

In summary, most physics theory arguments that would have been known in 1942 comparing the DT and DD fusion cross-section magnitudes (in the absence of a DT resonance) do not lead to the expectation of a higher DT cross section. The only phenomenon that enhances the DT cross section is the aforementioned phase-space argument based on the higher $\mathit{Q}$-value compared with DD reactions, but even there, the enhancement is only of order a factor of 2. The most compelling hypothesis for Konopinski’s inspired suggestion remains his knowledge of the 1938 Ruhlig experimental paper^[25] and Rutherford’s 1937 paper,^[23] as discussed in Sec. IV.A.2.a.

IV.A.4. Oppenheimer’s 1942 Berkeley Summary Memorandum

Following the July 1942 Berkeley conference, on August 20, 1942, Oppenheimer wrote a summary, “Memorandum on Nuclear Reactions,”^[79,80] regarding the feasibility of a hydrogen bomb.^s As mentioned earlier, Oppenheimer’s memorandum communicated a surprisingly high level of confidence, saying it was “guaranteed to work.” Although Oppenheimer was the sole author of this memorandum, it reflected the deliberations of the theorists present that included Teller, Bethe, and Konopinski.

The focus was not on the benefits of adding tritium to the deuterium TN fuel because tritium was scarce (Fermi’s reactor had not yet been taken to critical, and making tritium in a reactor would have to compete with the immediate priority of using reactors to breed plutonium); rather, it was on in situ breeding of tritium in the deuterium fuel and then reaping the benefits via secondary nuclear reactions. Tritium (and ³He) are created from the DDp (and DDn) reactions and, in turn, react with more deuterium to create more energy. This idea must have followed Konopinski’s statements at the conference on the potentially valuable role of tritium, and furthermore, it seems likely that the focus on secondary reactions must, via Konopinski, have been influenced by Ruhlig’s 1938 paper,^[25] which also discussed secondary reactions, in which tritium is first bred and then reacts, Sec. IV.A.2.

Oppenheimer gives the four reactions involved in burning deuterium as D$(\mathit{d},\mathit{p})$T and D$(\mathit{d},\mathit{n})$³He, and the subsequent secondary reactions D$(\mathit{t},\mathit{n})\mathit{\alpha }$ and D(³He,$\mathit{p}$)α. Note the latter reaction would be expected to be less effective owing to the higher Coulomb barrier for the ³He reaction (see Sec. II.C.3).

Tritium and ³He breeding benefits energy production and represents a multiplication factor of 3 or 4, depending on assumptions, in the idealized scenarios that Oppenheimer considered for the summary memorandum, as we can see from the following argument. For deuterium-only burning, the energy release per DD pair is 3.65 MeV, averaging each of the DDn and DDp paths, or 1.8 MeV/D (the energy on a per-deuteron basis). But, using the four above-mentioned reactions, given by Oppenheimer in the memorandum, and including the secondary reactions, one finds that the four reactions produce 43.2 MeV from six deuterons:

(14) $6\mathit{D}\to 2\mathit{n}+2\mathit{p}+2\mathit{\alpha }+Q_4\mathrm{,}$(14)

where $Q_4=Q_{\mathit{DDn}}+Q_{\mathit{DDp}}+Q_{\mathit{DTn}}+Q_{D^3\mathit{He}}\approx 43.2$ MeV, where we have read the values for $\mathit{Q}$ for each reaction from Table I. On a per-deuteron basis, this corresponds to 43.2 MeV/6 D or 7.2 MeV/D, with an energy-release multiplier of of 4, compared to the 1.8 MeV/D released in DD-only burning. If one takes credit for the secondary DT reaction but not the D³He reaction, owing to its higher Coulomb barrier, one instead gets a three-reaction relation:

(15) $5\mathit{D}\to 2\mathit{n}+\mathit{p}+\mathit{\alpha }{+}^3\mathit{He}+Q_3\mathrm{,}$(15)

where $Q_3=Q_{\mathit{DDn}}+Q_{\mathit{DDp}}+Q_{\mathit{DTn}}\approx 24.8$ MeV, or 5 MeV/D, providing a benefit of a factor of a little less than about 3 compared to deuterium-only burning. Oppenheimer’s memorandum quotes an energy release of 2.8 $\times$ 10¹⁸ ergs/g of D, which is equivalent to 5.8 MeV/D, which is a value similar to the latter value. But, it seems most likely that Oppenheimer’s 5.8 MeV/D was instead simply a calculational error, as he explicitly states that the cycle of four reactions he considers ultimately converts 3D to one proton, one neutron, and one $\mathit{\alpha }$. This can be seen by dividing Eq. (14)(14) $6\mathit{D}\to 2\mathit{n}+2\mathit{p}+2\mathit{\alpha }+Q_4\mathrm{,}$(14) by two, giving 7.2 MeV/D as stated above. The numerical values given above are for an idealized, and most optimistic, case wherein all the constituents react with unit probabiity. Later, in Fermi’s 1945 lectures on the Super,^[103] calculations more realistically quantify the benefits of these secondary reactions.

The 1945–1946 patent, S-680X, by Teller, Oppenheimer, Konopinski, and Bethe^[82] cites the earlier 1942 Oppenheimer summary and expands on its logic.^t Following deuterium-deuterium reactions, it states: “Because of the high speeds of the product nuclei, the above reactions … are followed by secondary reactions such as DT, D³He.” Therefore, the authors were not just thinking of the benefits of a higher DT cross section, but they explicitly note a higher secondary triton energy, from the reaction recoil, to better overcome the DT Coulomb barrier repulsion in secondary reactions. The deleterious effect of slowing down of the charged particles prior to a secondary reaction was not discussed, although Fermi did discuss this in his 1945 lectures.^[103]

This August 1942 Oppenheimer document appears to be the earliest reference for the idea of breeding tritium within the fuel. This concept would be extended in the 1945 time frame by Teller et al. when suggesting the value of ⁶Li as a fuel to breed tritium.

IV.B. German Fusion Research

German wartime nuclear research has been documented in numerous books, including Goudsmit’s Alsos,^[104] Irving’s The Virus House: Nazi Germany’s Atomic Research and the Allied Counter-Measures (also called The Virus House),^[105] Walker’s “German National Socialism and the Quest for Nuclear Power, 1939–49,”^[106] Powers’s Heisenberg’s War: The Secret History of the German Bomb,^[107] Carson’s “Heisenberg in the Atomic Age: Science and the Public Sphere,”^[108] and Bernstein’s Hitler’s Uranium Club.^[109] Here, we briefly comment on aspects that go beyond Germany’s desire to create a fission bomb, to their early ideas on harnessing fusion.

Allied concerns that Germany could have TN as well as fission bomb ambitions were natural given the history of German expertise in this area. In Sec. I, we described how the earliest theoretical insights into TN fusion came from Germany, even though the first experimental demonstrations were in Britain, at Cambridge. Furthermore, as will be discussed below, in the late 1930s and 1940s, U.S. scientists made much use of seminal German 1930s measurements on light-hydrogen-ion stopping powers to help infer TD and DD cross sections from their thick-target neutron production measurements. These came from Gerthsen and collaborators, from Tubingen, and were used by Bethe and his collaborators at Los Alamos.

Intelligence on Germany’s heavy water effort for Heisenberg’s atomic weapons work was provided to the United States by Britain. On June 19, 1942, Vannevar Bush of the OSRD reported to Major General Strong that he had heard from a representative of the British Government that they “have learned of the existence of a plant in Norway for the production of heavy water, and that this is being shipped to Germany”^[30] (as previously mentioned in Sec. IV.A). There was a subsequent communication on August 18, 1942, by Britain’s W. A. Akers,^u who led the Tube Alloys atomic weapon effort, to the U.S.’s Conant. The letter focused on German goals to make a heavy water power plant: “It seems obvious to us that Heisenberg would be put in charge of this work and we have known for some time that heavy water is being moved from Norway to Germany, although we have not succeeded in tracing it right up to Heisenberg.”^[30]

Hoddeson et al.’s Critical Assembly: A Technical History of Los Alamos During the Oppenheimer Years, 1943–1945^[71] describes how at the July 1942 Berkeley conference,

Teller pointed out that deuterium would be far cheaper to obtain than ²³⁵U or ²³⁹Pu…. From that point on, although Oppenheimer tried to bring the discussion back to the fission bomb, Bethe and others spent much of their time at the meeting talking with Teller about his Super ideas. Bethe recalls Teller being so preoccupied with the Super that at one point, in a discussion of the Germans’ desire for heavy water (as a moderator in the nuclear reactor), “Teller as usual jumped thirty years ahead of time and said, ‘Of course they want heavy water to make a Super.’”

Here, Bethe suggests that Teller’s concerns about a German hydrogen bomb were far fetched for 1942, yet we will see that this concern was shared by others and that, indeed, Germany did pursue (and failed in) such ambitions.

The aforementioned September 18, 1942, letter from Compton to Conant^[74] stated:

I should add that the possibility of a thermonuclear explosion has been recognized for some years. It was investigated by Szilard who dropped the subject because he found no practical method of detonating the explosion. Fermi discussed this possibility freely with his colleagues engaged upon this work in 1939. These good colleagues would include Teller, Wigner, Wheeler, and probably others. Any evidence of our special interest in the neutron characteristics of deuterium might lead to the suspicion that we have found some practical method for this using the material. This statement, however, does not apply to experiments on heavy water, which has its own use in connection with concentrated power plants. It is reasonable to suppose that the Germans will have considered the possibility of thermal nuclear [sic] explosions, but it is very possible that they may have never demonstrated theoretically its feasibility.

On December 15, 1942, Vannevar Bush wrote^[30] to the U.S. vice president, secretary of war, and chief of staff:

We do know that Germany started work along these general lines in 1939. We also know that, after the fall of Norway, the product of a Norwegian plant producing heavy water was increased and the products shipped to Germany, and heavy water is at the basis of one of the most promising methods of proceeding towards power uses, and, as has been realized more recently, also towards an explosive.

Irving’s book^[105] and Kunkle’s report^[110] provide a summary of wartime German experiments that aimed—and failed—to produce fusion processes.

IV.C. Soviet Fusion Research

Many authors have written on the history of Soviet nuclear weapons development. David Holloway’s Stalin and the Bomb^[111] provides a comprehensive summary, as do Richard Rhodes’s books,^[20,112] and of course, Sakharov’s Memoirs^[113] should be read. Frank Close’s Trinity: The Treachery and Pursuit of the Most Dangerous Spy in History^[114] also describes aspects of Soviet work through the lens of Klaus Fuchs’s espionage.

Although the Soviet scientists made remarkable breakthroughs for their H-bomb program through independent research, it appears that they relied on U.S. data on basic nuclear fusion cross sections transmitted to them by Fuchs, at least during the 1940s and early 1950s. Goncharov has described^[115] how the DT cross-section data used in Russian calculations in the late 1940s were from the U.S. experiments (see Sec. V.C) passed to them by Fuchs in 1948. He notes the “irony” that the United States decided to publish these same Los Alamos Bretscher-French DT cross-section data in the open in Physical Review, April 15, 1949,^[53] soon after Beria had been finally persuaded to broaden the access list of Russian scientists who needed these data for their calculations. Indeed, Goncharov goes on to say that their calculations using the large DT cross section obtained from the United States led them to believe that the technology they had been planning to use for their first H-bomb test would work. Also, Fuchs’s 1950 confession to the British scientist and interrogator Michael Perrin included statements^[111] that Fuchs passed on “the TD cross section value before this was declassified.” The United States declassified these data because of the benefits for developing peaceful fusion energy technologies. The Churchill Archives Center, Cambridge, holds correspondence between Bretscher (in the United Kingdom) and Teller regarding U.S. classification decisions in the late 1940s that enabled each of them to publish parts of their earlier research from Los Alamos in Physical Review, in 1948–1949.

It is beyond the scope of this paper to describe later Soviet measurements of TN cross sections in any detail. From Bosch and Hale’s 1992 review,^[38] it is evident that Soviet scientists were publishing their own higher-quality TN measurements after the mid-1950s.

V. DT AND DD CROSS SECTIONS, 1942–1952

V.A. Chicago Met Lab, DD, 1942

The DD Chicago measurements began in 1942, as can be inferred from Hawkins’s history.^[88] A Cockcroft-Walton accelerator was used to accelerate deuterons onto a heavy water (ice) thick target. The thick-target data relied on estimates of the stopping power of deuterons in ice, as described later for the 1945–1946 Los Alamos measurements that also used thick targets of heavy water (ice). This was recognized to be a substantial uncertainty in the cross-section assessments, and indeed, the later, April 14, 1944, publication date of the Chicago measurements reflects the fact that the early results were subsequently revised once an updated assessment of the stopping powers came from Ashkin et al. in their September 23, 1943, report, LA-12-R^[116] (see Appendix A). For example, CF-1564, Table II,^[118] shows how the D₂O stopping power at 119 keV was increased by 30% to the value in LA-12-R, increasing the Chicago DDn cross section accordingly. Later in this paper, the early values from Chicago, before they were revised up by 35% to 45%, can be seen in Table IV, where they influenced the DDn cross-section evaluation by Bethe and Christy in the first Los Alamos “Handbook of Nuclear Physics,” LA-11.^[26]

TABLE II DDn Cross-Section Data from Coon et al., Chicago, as Published in 1944, Compared with Modern ENDF*

Energy (Laboratory) (keV)	DDn Coon et al. 1944^[Citation118] (b)	ENDF/B-VIII.0 2018^[Citation35] (b)
119	2.47E-02	2.10E-02
171	3.68E-02	3.10E-02
220	5.13E-02	4.10E-02
294	8.35E-02	5.20E-02

*Early assessments of these data in 1943 were lower, owing to different stopping powers assumed in the thick-target experiments

The Chicago results were impressive for their time. Compared with modern evaluations, between 122 and 300 keV, the DDn measurement was high by just 15% to 30%, and the DDp was high by 20% to 60%; see Tables II and III. The data confirmed Oliphant’s 1934 observation that the DDn neutron branch and the DDp proton branch are similar in magnitude, as expected theoretically.

TABLE III DDp Cross-Section Data from Coon et al., Chicago, as Published in 1944, Compared with Modern ENDF*

Energy (Laboratory) (keV)	DDp Coon et al. 1944^[Citation117] (b)	ENDF/B-VIII.0 2018^[Citation35] (b)
122	2.63E-02	1.95E-02
171	3.26–02	2.84E-02
219	4.17E-02	3.58E-02
300	5.16E-02	4.50E-02

*Early assessments of these data in 1943 were lower, owing to different stopping powers assumed in the thick-target experiments.

Later in this paper (Sec. V.C), these results are compared with other data sets and evaluations. Bretscher and Konopinski’s 1947 review of the Chicago data^[28] discussed open questions that substantially affected the inferred cross-section values, i.e., the best way to assess the rate of change of the measured neutron yield with incident deuteron energy given the sparse data set and stopping powers of deuterons in the thick target. The DDn estimates in Fermi’s 1945 lectures were informed by these measurements, along with Bretscher’s Los Alamos measurements at the lower energies (see later).

The Chicago CF reports cite earlier work, for example, at Iowa State University for DDp and various laboratories for DDn, though it is not clear that any of these were viewed as reliable. They also cite 1937 DD measurements of neutron yield published in Physical Review, work at the Carnegie Institution of Washington by Amaldi et al.^[119] and at Princeton by Ladenburg and Kanner.^[120]

V.B. Purdue, TD, and ³HeD, 1942–1943

The earliest measurement of the TD cross section was at Purdue under contract for the Manhattan Engineering District (Manhattan Project) war effort, beginning late in 1942 and extending into fall 1943. (Margaret Gowing’s history^[121] erroneously says that the Bretscher 1944–1946 Los Alamos measurements were the first-ever measurements of DT.) See Sec. IV.A.1 for a description of how the motivation for this experiment came from Bethe, at Oppenheimer’s July–August 1942 Berkeley conference.

The OSRD contract with Purdue is shown in Fig. 19. Although the Manhattan Project was focused in 1943 on nuclear fission processes, this contract notes the “efficient form of a bomb” that was being explored, using fusion.

Fig. 19. The OSRD contract with Purdue to measure the DT cross section.^[30]

Note the security consideration in Fig. 19: “Work also can be carried out there without attracting the attention of other nuclear physicists.” In fact, on October 12, 1942, Oppenheimer had written to Holloway^[30]:

I had occasion to see Bethe in Cambridge and he told me that he had given to you rather full information on the motivation for the mass 3 experiments. I should like to make it clear that neither he nor I nor anyone else was authorized to give you this information. I understand, of course, that it will help you in the prosecution of the work to know how important are the issues which will be settled, and to have a feeling of the background of the problem; and obviously I can not ask you to forget things that you know. Nevertheless, I should like, in the most urgent and serious way I can, to ensure you of the necessity for secrecy. I think that you will have imagination enough to see that the information which you possess could do us irreparable harm if it were to fall into the wrong hands.

Baker and Holloway came from Cornell to lead the work and were joined by King and Schreiber at Purdue. Tritium was provided by Segrè, Kahn, and Kamen from the Berkeley cyclotron, using deuteron bombardment on heavy water. The tritium ions were accelerated and bombarded deuterium in a heavy water (ice) target. They measured the cross section at incident laboratory triton energies of 200 to 600 keV. While this was a foundational experiment, the authors were unable to probe the very important lower-energy region of tens of kilo-electron-volts, which would come later in 1945–1946 at Los Alamos.^[52,55]

The ³He-D cross section was measured first and published in Los Alamos report LAMS-2^[101] on June 27, 1943, and the TD cross section was published on September 17, 1943, as report LAMS-11.^[89] The latter paper on the TD measurement says that the experiments yielding data were performed between August 21 and September 3, 1943, and describes the numerous complications they encountered in performing T experiments versus ³He experiments. It is a reflection of the urgency of the wartime environment that the paper was published (internally) just 2 weeks after the data were taken. Although these Los Alamos reports were initially classified, they have been available as unclassified reports from Los Alamos’s library for many years.

This foundational experiment obtained a large TD cross section that peaked at 2.8 b at a triton incident laboratory energy of 320 keV. (In fact, we now know that they were off: The correct magnitude peaks at 5 b, and the energy of the resonance in the incident tritium frame is at 3/2 $\times$ 108 = 162 keV, which is a factor of 2 lower). It is notable that the paper did not loudly proclaim that it was the first measurement of this important cross section nor did it comment on the very large magnitude of the cross section obtained. But, as described below, owing to the presence of the resonance in the A = 5 system, the large magnitude got their (and Bethe’s) attention. The written record does not explicitly describe the inference of a resonance until Bretscher and French’s subsequent 1945–1946 Los Alamos papers.^[52,55]

The Purdue measurements, like those around the same time frame at Chicago (DD) and a little later at Los Alamos (DD and TD), were thick-target-yield measurements that required knowledge of stopping powers of the incident ions on the heavy water (ice) targets. How they determined the stopping powers will be described later, in the section on the Los Alamos experiments (Sec. V.C) and in Appendix A. The Purdue cross sections were shown by Fermi in his 1945 Los Alamos lectures; see Fig. 20. Quantitative comparisons of these first DT data with later measurements and with evaluations are given later in the paper; see Fig. 21. They are seen to be impressively accurate for the time.

Fig. 20. A reproduction of Fermi’s figure from his 1945 Los Alamos lectures, showing the DT cross section versus the incident laboratory triton energy. The DT cross section has the 1/E and exponential penetrability terms divided out, as is done in an S-factor representation. The three experimental points at the lower energies, near 20 to 30 keV, were preliminary (1945) Los Alamos Bretscher values; the higher data set, around 200 to 600 keV, comprises the 1943 Purdue values of Baker and Holloway.

Fig. 21. DT (black curve), DDn (red curve), and DDp (blue curve) fusion cross sections compared with 1940s–1950s data and with the ENDF/B-VIII.0 evaluation (solid curves) from the R-matrix analysis of all known data. The DT data are from Purdue (PU 1943, two sets; see text),^[89] Los Alamos (LA 1946)^[53,55] and (LA 1952)^[33,34]) The DDn data are the Chicago Met Lab (ML 1943)^[26,118] and Los Alamos (LA 1952).^[34] The DDp data are the Chicago Met Lab (ML 1943)^[117] and Los Alamos (LA 1946)^[52] and (LA 1952).^[34] The R-matrix analysis is, additionally, strongly constrained by other data (not shown), including the very accurate 1980s–1990 data by Brown and Jarmie^[45] and Jarmie et al.^[122]

V.B.1. Purdue Historians’ Account

Purdue’s wartime contributions have been described by Gartenhaus et al., “A History of Physics at Purdue: The War Period (1941–1945),”^[90] which is based on a private communication between S. Gartenhaus and R. E. Schreiber, one of the coauthors of the key DT and D-³He papers. We provide below a verbatim quotation from this interesting web article:

The physics building was dedicated as the Charles Benedict Stuart Laboratory for Applied Physics during a two day conference on problems of modern physics that was held on June 19–20, 1942, at Purdue. At almost the same time, two young instructors in the department, Drs. L.D.P. King and R.E. Schreiber, assisted by a number of graduate students, were completing the year-long task of dismantling the cyclotron, transporting the components from the old to the new building, reassembling it and putting it back into operating condition. With this task completed and with America’s entry into World War II six months earlier the future of these two instructors as nuclear physicists was somewhat cloudy. However, a variety of things were in the wind and at the urging of Karl Lark-Horovitz, who hinted at the possibility of a new nuclear project of some type, the two decided to stay with the cyclotron.

What happened next is best described in the words of one of the two instructors, R. E. Schreiber^v:

The first intimation that King and I had of this nuclear project was a meeting attended by K. Lark Horovitz, Hans Bethe, Marshall Holloway and the two of us. Dr. Bethe was already well known at the time as a nuclear theorist at Cornell. Dr. Holloway, although unknown to us was introduced to us as the chief investigator of an experiment that might make use of the Purdue cyclotron and which would be very important to the war effort. If we agreed to participate, we would be relieved of our teaching duties and would be spending full time on the project. We were given no further details until we agreed to participate and each of us had signed a secrecy agreement. We both agreed and very soon, Drs. Holloway, and Charles P. Baker, both from Cornell University moved to West Lafayette, and we started work on the project.

Our first task was to seal off the cyclotron laboratory with locked doors and barred windows and to hire a security guard. We were then told that what was desired was the lowest energy possible from the cyclotron that would produce a reasonable monoenergetic beam. This was a blow to King and me since we had been working for many weeks to set the cyclotron to produce particles of the highest possible energy. However, we went to work, installed induction coils in the oscillator circuit to slow it down, reduced the magnetic field and completely retuned the system to get down from about 10 MeV to the range of 0.5 to 1 MeV.

Once this was accomplished we were finally told of the experiments that we were to carry out.

King and Schreiber were not aware at the time, of course, of the overall picture. They were simply told that the purpose of the Purdue experiment was to measure the cross section, as a function of the bombarding energy, of the fusion of a deuterium nucleus, when bombarded with a tritium nucleus to form 2He⁴….In the usual nuclear physics notation, the two reactions they were to study were respectively:

D(T,α)N; D(2He³,α)P.

These two experiments were conducted with the Purdue cyclotron during 1942–1943 and were published in the classified literature as Los Alamos Technical reports, numbered LAMS-11 and LAMS-2, respectively. Interestingly enough, even though these reports were classified as secret the particles were not identified in the reports but were encoded by the scheme: D = 20; T = 30; α = 240; 2He³ = 230. Both reports were eventually declassified but only long after the end of the war.

To be sure King and Schreiber did not know, at the time, why the two cross sections they were measuring were important nor how they fitted into the overall plan. For that they had to wait until 1943 when they were invited to—and subsequently transferred to—Los Alamos.

One of the important problems that the four researchers had to solve, immediately, was that of obtaining the materials for conducting these experiments. Deuterium, although very expensive at the time was readily available in the form of a bottle of gas and it was decided to use it as the target material. Tritium, on the other hand, is a radioactive isotope of hydrogen with a relatively short half-life and thus had to be produced artificially by bombarding other materials. As described by R.E. Schreiber:

Our supply of tritium, we were told, was obtained by dissolving a beryllium target [MBC: other sources have this as a heavy water target] that had been bombarded by the Berkeley cyclotron, and was probably the largest sample of tritium in the world. The tritium itself came to us in the form of a gas sealed into a small glass capsule. Small amounts of this tritium gas were then carefully metered out and mixed with enough ordinary hydrogen to serve as a feed gas for the ion source of the Purdue cyclotron. With the proper adjustment of the cyclotron, only the tritium ions were accelerated to the appropriate energy and the ordinary hydrogen was scavenged by the cyclotron pumping system.

With the proper adjustments of the cyclotron a beam of energetic tritium ions would spiral out from the ion source, gain energy with each revolution, and finally be extracted and led into the target chamber. Electrodes placed in the chamber detected the very tiny pulses from the tritium ions and the much larger pulses when fusion occurred. Tedious but straightforward calibrations and calculations eventually yielded the cross section values.

The 2He³ experiment was very similar, our supply being helium by-products from a liquid air plant. Dr. A.O.C. Nier of the University of Minnesota carefully processed this helium to enrich its He³ content. Again we were the custodians of a very rare and valuable material.

Due to the energy spread of the beam coming out of the cyclotron, our cross section measurements were fairly crude but gave some unexpected and surprising results. The deuterium-tritium cross section was very large and peaked at a fraction of an MeV. Dr. Hans Bethe, was in frequent communication with us about these measurements and for a time he simply did not believe our results, since our data indicated a “resonance” reaction of a type inconsistent with theoretical calculations. (It was at this time that the term “barn” was defined as a unit for cross section data. Since some communication was often by telephone, use of technical terms was strictly enjoined. Thus it was agreed that the “barn” should be used instead of 10^–24 cm² since a cross section that large was indeed “as big as a barn.”)

Eventually, Dr. Bethe was convinced that our peak value for the DT reaction of 2.8 barns was valid. So in September 1943 we shut down, restored the cyclotron to its original 10 MeV configuration, turned it over to Don Tendan and shipped all classified materials to Project Y.

We had been contacted earlier in 1943 with an invitation to join Project Y, “near Santa Fe, New Mexico.” At that time we still did not know the real objective of the project but knew that many prominent nuclear physicists were involved. It took some serious discussions with our wives and with each other but eventually we all agreed to take the plunge. Upon arrival at Los Alamos we were finally told what the Manhattan Project was all about and that we were, as a team, to design, build and operate the world’s first enriched uranium reactor.

With regard to the remaining members of the Purdue physics department, at some point in late fall of 1943, nearly two-thirds of the faculty and graduate students engaged in nuclear research at Purdue, simply vanished from the campus all leaving behind the same post office box as a forwarding address. The locals of course, had no idea where they went, but assumed naturally that it was somehow related to the war effort. Only much later did they discover that Los Alamos, New Mexico, had been their destination.

As noted earlier, these 1943 first-ever DT fusion cross-section measurements were impressively accurate, as seen in Fig. 21 [the data labeled as “PU (1943)”].

A Purdue researcher who worked on these TN cross sections and moved to Los Alamos was L. D. Percival King, who subsequently had a career in nuclear reactor physics and nuclear criticality. His son, Nicholas (Nick) S. P. King also had an influential career at Los Alamos in nuclear diagnostics, nuclear science, and proton radiography. As a boy, Nick was featured in a nice photograph with Bethe and Fermi in the Jemez mountains above Los Alamos, Fig. 22.

Fig. 22. Bethe and Fermi with boys Nick King and Paul Teller in the Jemez mountains, New Mexico, 1946. Photograph by L. D. P. King, collaborator on the first-ever DT cross-section measurement (1943).

V.C. Los Alamos, TD and DD, 1943–1951

V.C.1. First Handbook of Nuclear Physics, LA-11, 1943

Once researchers moved to Los Alamos in 1943, the current understanding of nuclear cross sections was tabulated by Bethe and Christy in the first “Los Alamos Handbook of Nuclear Physics,” LA-11,^[26] There, their evaluated DDn cross section was represented in a figure, informed by the Chicago DDn thick-target absolute data below 300 keV, Heydenburg’s 0.9-MeV thick-target absolute data from the Carnegie Institution of Washington (CF-604), and a Rice (relative) thin-target measurement for deuterons above 500 keV (CF-350); see Table IV. This Los Alamos handbook is a historically interesting document, for it shows the early values from Chicago before they were revised upward by 35% to 45%, presumably based on changes to the assessed D₂O target stopping powers. The table shows that this first DDn evaluation in 1943 was roughly within 20% of our current understanding at laboratory energies below 300 keV.

TABLE IV Cross-Section Values for DDn from Bethe and Christy’s Los Alamos Handbook, LA-11 (1943)^[26]*

Energy (Labotatory) (keV)	Bethe and Christy LA-11 (1943) (mb)	Coon et al. Initial (1943) (mb)	Coon et al. Final (1944) (mb)	ENDF/B VIII.0 (mb)
40	5.0			2.7
119	17.0	17.0	24.7	21.0
171	26.0	26.0	36.8	31.0
220	37.0	37.0	51.3	41.0
294	63.0	63.0	83.5	52.0
500	98.0			52.5
1000	136.0			93.6
2000	178.0			104.0

*Below 300 keV, the cross sections derive from early values from Chicago, which were later increased by 35% to 45%. Modern ENDF/B-VIII.0 values are shown for comparison.

V.C.2. Bretscher’s 1945–1946 Experiments

Oppenheimer’s priority at Los Alamos was the development of the fission bomb; fusion research efforts were modest and were motivated by Teller and supported by Oppenheimer. Researchers from the British Mission to the Manhattan Project had a particularly important role in the TN fusion cross-section measurements in Fermi’s advanced concepts F Division. Cambridge’s Egon Bretscher (Fig. 23) and his students Anthony French and M. J. Poole worked at Los Alamos through 1946 and then returned to England. Oxford’s James Tuck was focused mostly on high-explosives research during the Manhattan Project (helping invent the implosion system used in Fat Man^[123]), but after returning to Britain, Tuck came back to Los Alamos’s Physics Division and made major advances to the accurate measurement of TN cross sections.

Fig. 23. Egon Bretscher (foreground, left) and Robert Serber (foreground, right) at the 1946 Nuclear Physics Conference held in Los Alamos.

One can speculate why the F-3 group in Fermi’s F Division was staffed by the British for TN measurements, which is a decision that must have had support from both Oppenheimer and Chadwick. As the Manhattan Project ramped up in 1943, the focus was on fission. Most of the British were only authorized to come to Los Alamos in 1944, and by this time, the fission experiments were well underway, being executed by a very able set of U.S. experimentalists. Thus, even though Cambridge’s Bretscher and French had been working on fission before coming to Los Alamos, they could be assigned instead to support Teller’s TN interests. Thermonuclear physics was not new territory for them. A standard way to make source neutrons for fission cross-section experiments, employed by experimentalists in Britain, Germany, and America, was using an accelerated D-on-D target-source reaction, which could create quasi-monoenergetic neutrons up to a few mega-electron-volts. Bretscher and French had been doing this in Cambridge, and indeed, Cambridge was where accelerator-based fusion reactions were first produced. Their assignment now became the precise characterization of such reactions to obtain TN fusion cross-section data.

Bretscher was the lead for the TD and DD measurements at Los Alamos in 1945–1946, using the “high-voltage set” kenotron rectifier accelerator that he installed.^[52,55] The experiments also involved the development of suitable ion sources, a vacuum system, and methods for handling and recovering the small amounts of tritium, only “a few cc,” that they were given. The tritium would have come from Oak Ridge’s Clinton piles. In May 1944, Oppenheimer discussed with Groves the need for tritium production, which led to an agreement to use “surplus neutrons in the Clinton piles”^[88]; tritium was being produced at a rate of 4 mL/month by February 1945^[124] (later it was produced at Hanford^[125]). Compared with the earlier Purdue (TD) and Chicago (DD) measurements, the Los Alamos measurements successfully extended the energy range down to 15 to 105 keV, which is an important range for TN applications. Bretscher wrote the chapter on cross sections in the “Super Handbook,” written in October 1945, and his results were quoted in Fermi’s famous lectures from the same time (see Fig. 20). The results of his DD and DT fusion measurements were documented in internal Los Alamos reports in September and November 1946,^[52,55] before he returned to England. In 1947, Bretscher cowrote (with Konopinski) the chapter on TN cross sections in Robert Wilson’s magnum opus, “Nuclear Physics,” LA-1009. This summed up everything learned during the Manhattan Project, and with French, Bretscher wrote Physical Review articles in 1948 and 1949,^[53,126] when these data were declassified.

As in the earlier Chicago and Purdue measurements, Bretscher and French measured thick-target neutron production on solid heavy water (ice) targets as a function of incident energy. With knowledge of the stopping powers for incident deuterons and tritons, they could determine the cross sections in the following way:

(16) $\mathit{\sigma }(\mathit{E})=\frac{1}{A}\mathrm{.}\frac{\mathit{dN}}{\mathit{dE}}\mathrm{.}\frac{\mathit{dE}}{\mathit{dx}},$(16)

where the constant $\mathit{A}$ contains the product of the number of incident projectile ions per unit of beam current and the number of deuterium nuclei per cubic centimeter in the target. The term $\mathit{dN}/\mathit{dE}$ is the rate of change of the measured fusion secondary particle production with incident ion energy, and $\mathit{dE}/\mathit{dx}$ is the evaluated stopping power as a function of ion energy. The measurements were made at a range of incident energies $\mathit{E}$, so that $\mathit{dN}/\mathit{dE}$ could be evaluated from the slope of the data; some of the challenges with this approach are described in Appendix A.

Unlike the earlier Purdue measurements of TD, the Los Alamos measurements now used tritium made from reactors with the ⁶Li(n,t) reaction, and their accelerator enabled them to extend the measurements to lower energies, down to 15 keV.

V.C.2.a. Fermi’s Division Monthly Progress Reports

The NSRC archives at Los Alamos hold the monthly progress reports written between March and October 1945.^[127] Bretscher, as a group leader, authored the group F-3 reports. Given that this was an intense time at Los Alamos—involving finalizing the fission bomb designs, their manufacture, the Trinity test, interpretation of the Trinity diagnostic data, and the employment of two weapons in war—it is impressive that the scientists took the time to carefully document their ongoing nuclear physics fusion research work.

The efforts documented during this time are as follows. In March 1945, the equipment was being installed, and in April, it was being “run in.” The DDp reaction was first measured in May between 10 and 40 keV laboratory energies. They had hoped to measure both the DDp and DDn channels, but for some reason, the latter did not work out. Regarding their DDp data at 10 to 40 keV, they commented that their data agreed with an extrapolation down from the Chicago Met Lab’s 1942–1944 data in CF1564 (described in Sec. V.A^[117]). In June, DDp angular distributions were measured, which would later provide information for studies and publications on the underlying physics of few-body reactions.

July 1945 was the month when TD data were first measured, at a triton laboratory energy of 40 keV with a 0.01-μA beam containing tritons incident on a heavy-ice target. This work utilized a vial containing ordinary hydrogen and 0.2 mL of T gas. The July progress report states, “Large numbers of alphas were observed, when the beam of 40 keV of energy and 0.01 microamp was directed onto a target of D₂O.” They measured the cross section and found an angular distribution that is approximately isotropic. Between August and October, more data were taken, and new “KR3 and KR5” kenotron accelerating components were added, allowing measurements up to 100 and then 150 keV. The 100-fold increase in DT cross sections compared with DD would have been first observed when they reached the highest DT measurement energies that they made, 125 keV, in this August–October 1945 time frame (when the c.m. energy, 50 keV, was approaching the resonant maximum energy at 65 keV).

A detailed characterization of the DT resonance was given in Bretscher and French’s Los Alamos report LA-582, dated November 15, 1946.^[55] An image extract is given in Fig. 24, and one can see that this document is identical to the 1949 version published in Physical Review.^[128] Although Bretscher was the first to document and quantify the resonance’s energy, we think it very likely that Bethe would have recognized the likely presence of a resonance as early as 1943, when the first DT cross-section data were obtained at Purdue^[3,129] (though at energies above the resonance’s peak). The spin of the resonance was correctly identified by 1952^[54]; see our discussion on the evolving understanding of the 3/2⁺ resonance in Sec. II.C.

Fig. 24. An extract from Bretscher and French’s paper LA-582,^[55] November 15, 1946, providing the first identification of the DT resonance.

While Bretscher is generally credited with correctly anticipating the properties of ²³⁹Pu,^[9,129] his discovery of the DT resonance has gone largely unappreciated. His 1945–1946 measurements^[128] have been cited only 54 times, compared with the 460 citations of Hoyle’s paper. Strangely, this is similar to the fact that the first-ever observation of DT fusion, in 1938 by Ruhlig,^[25] had never been cited for DT until our recent paper^[3]! It is with this context that we proposed^[4] the naming of the 3/2⁺ DT resonance as the “Bretscher state,” in the spirit of its being anthropically important, like the Hoyle state.

It is a surprise to us that in all this documentation—monthly progress reports, laboratory reports, and journal publications—zero excitement is communicated regarding the very large DT resonant enhancement. A DT fusion cross section as large as 5 b is really quite staggering; fast neutron fission cross sections for uranium and plutonium are of the order 1 to 2 b, and that is for actinide nuclei that are so much larger! The laconic tone in the written documentation is at odds with the more-natural, excited, and emotional response to the discovery recalled by French in a transcribed oral history.

V.C.2.b. Oral History Interview

Anthony French was interviewed by Theresa Strottman in 1992,^[130] and his recollections of the TD “discovery event” are worth quoting. However, his memory is not correct in all regards. He recollects his measurements as providing the first-ever TD data. We know that by this time (1944–1945), the Purdue measurements had already been completed and published in the 1943 Los Alamos report LAMS-11,^[89] where the large DT cross section had been discovered, albeit at higher triton energies of a few hundreds of kilo-electron-volts and with poor energy resolution. Hawkins’s contemporaneous Project Y history recounted that “the tritium cross section, however, was very much larger than had been anticipated at energies of interest.”^[88] Perhaps the surprise that French relates below was because their very low-energy measurements were so far below both the resonance energy and the DT Coulomb barrier. Their initial laboratory triton energies were in the 20- to 40-keV region, corresponding to an available c.m. energy (×2/5) of 8 to 16 keV; this is far below the Coulomb barrier for TD fusion, which is near 300 keV (see Sec. IV.A.3). Here is an extract of that interview:

French:

So anyway, we were all set up to do these fundamental experiments. And nobody knew, despite what the theorists predicted, nobody knew what the tritium/deuterium reaction was going to be like. Then came the day when we, for the first time, put the tritium into the source of our accelerator in place of deuterium. And saw an absolute rain of pulses on the oscilloscope and we thought at first that something must be breaking down electrically because there were so many pulses. But we checked and it was for real and the implications of that were monstrous. It meant that the deuterium/tritium reaction was about 50 times more probable than the deuterium/deuterium reaction and that really made it, for the first time, seem that a Super bomb might become a possibility. So that was an amazing thing.

I know we turned off the machine and, in fact, my boss brought in, went and called for Hans Staub, who I just mentioned, to come and look at it with us. And, I know, we then turned on the machine again and Staub was there. And he was saying, “Jesus Christ.” (Laugh) We realized that something very momentous had happened.

Strottman:

And this was before the explosion of even the atom bomb. You already had the inkling of the H-bomb?

French:

Yes, that’s right. Yes, it was amazing to me that this whole thing had been launched before even the feasibility of the fission bomb had been proved.

Not only are we puzzled by French’s erroneous statement that his were the first TD measurements, we also do not know what he means when he says “despite what the theorists predicted,” for we have not found any documentation regarding what the theorists expected the DT cross sections to be (either small or large); see Sec. IV.A.3.

Presumably, it was these same Bretscher-French measurements of the large low-energy TD cross section that Bretscher and Cockcroft were referring to in their biographical memoir on Fermi^[131]:

During part of my stay at Los Alamos I was in charge of the experimental group of the division for advanced development, headed by Fermi. It is natural, therefore, that we had a good deal of contact with Fermi who took great interest in what we were doing. An incident which is very characteristic of Fermi occurred when some particularly important and surprising results were obtained. When I told Fermi about it, he said, “Please give me the experimental data and I will calculate the final result and if my calculations agree with you then probably the results obtained are correct.” It was very characteristic of Fermi that he would not accept an experimental result but try to find out in detail how it was obtained. He was always available for any discussion and when he reported about the work of the division he was always very generous and fair in allotting credit where it was due.

V.C.2.c. Bretscher-French TD Data, 1945–1946

We now present the Bretscher-French TD data, which were so important in that they extended the early Purdue measurements down to the 15-to 125-keV incident triton energy range, important in TN applications and below the resonance energy and Coulomb barrier. Their data were published in Los Alamos report LA-582, November 15, 1946, in which they first documented the resonance enhancements that they were observing.^[52,55] The data began to be accumulated in July 1945; in Fermi’s fall 1945 lectures, described below, the first initial values in the 20- to 30-keV triton energy range were quoted (see Fig. 20). These same results were subsequently included in the Bretscher-Konopinski, Chap. 9, LA-1011,^[28] of Wilson’s “Nuclear Physics,” LA-1009, documentation of all that was accomplished during the Manhattan Project.^[27] These data were later declassified and published in Physical Review, 75, 1154 (1949).^[53,128]

The Bretscher-French cross-section data were determined from their thick-target alpha-production data and the triton-on-D₂O stopping power values using Eq. (16)(16) $\mathit{\sigma }(\mathit{E})=\frac{1}{A}\mathrm{.}\frac{\mathit{dN}}{\mathit{dE}}\mathrm{.}\frac{\mathit{dE}}{\mathit{dx}},$(16) . It is noted that the stopping power estimates come from French’s LA-392.^[132] The numerical values tabulated in the 1946 LA-581 DD and LA-582 DT laboratory reports^[52,55] and the later Physical Review papers in 1948 (DD) and 1949 (DT)^[53,126] do indeed follow the LA-392 stopping powers, although there are some discrepancies: Few-percent differences with LA-392 are seen in some cases. Also, the figure labeled D-on-D₂O stopping powers shown in the DD papers^[52,126] actually seems to instead show the T-on-D₂O values. The numerical values follow the expected relationships whereby stopping powers are the same for an incident T and incident D with the same velocities (so stopping powers are equivalent for tritons with incident energy 3/2 of the deuteron energy and 3 times the proton energy).

The published TD cross-section data are shown in Fig. 25 as yellow points and compared with evaluated ENDF/B-VIII.0 values. They are seen to lie below our best estimates today: They are low by 15% at 100-keV triton energy, with the discrepancy increasing to 40% at the lowest energies. Still, for the first-ever measurement at these low energies, well below the Coulomb barrier height, this experiment was impressive. Bretscher suggested an analytic fit could be used for these data that included both a Gamow penetrability factor and a Breit-Wigner resonance factor, describing the TD cross section as a function of the incident laboratory triton energy:

(17) ${\sigma }_{\mathit{DT}}(\mathit{E})=\frac{1}{E}\frac{A}{((E_r-\mathit{E}{)}^2+{\Gamma }^2)}\mathit{exp}(-1.72/\sqrt{(}\mathit{E}))\mathrm{,}$(17)

Fig. 25. TD cross-section measurements at Los Alamos by Bretscher and French, 1945–1946, compared with various parameterizations of these data from this same time frame and with the modern ENDF/B-VIII.0 evaluation. It is evident that Fermi’s 1945 parameterization followed the early 1945 Bretscher data; see also Fig. 20.

in units of barns, where $\mathit{E}$ is the triton laboratory energy in mega-electron-volts, and the constant $\mathit{A}$ = 325 × 10^–3 b∙MeV³. The resonance peak is $E_R$ = 124.3 × 10^–3 MeV, and its width is $\mathrm{\Gamma }$ = 71.7 × 10^–3 MeV. This analytic parameterization describes the measured values very well indeed: Below 100 keV, they match to a few percent.

After presenting the above parameterization of his data, Bretscher says (p. 15 of LA-1011^[28] (1947) and p. 1159 of the 1949 Physical Review paper^[53]): “These values may give a rough idea of the true state of affairs, but it should be remembered that in deriving them one makes use of the rather doubtful values of dE/dx.” Here, he is pointing to the fact that the method to extract cross sections from thick-target experiments requires knowledge of the stopping power and that there was uncertainty associated with these values (see Appendix A). Regarding the location of the resonance, the above resonance parameterization gave 124 keV in the incident-triton laboratory energy frame. Bretscher also presented an alternative analysis approach that gave a value of 343 keV (Table V), and he provided various cautionary comments regarding both methods they employed. In a 1949 letter to Teller,^[134] Bretscher passed on the latest United Kingdom (Harwell) measurement for the energy of the resonance, saying, “I hope that when you were here you saw Poole who has now established the position of the resonance of the TD reaction at, I believe, 140 kV triton energy.” (Allan and Poole published quite an accurate value, 155 keV, in Nature that year.^[133]) Today, we know from an EDA5 R-matrix analysis of data that the resonance is at an energy of 162 keV laboratory triton energy (×2/3 = 108 keV in the deuteron-incident system), which is a value that lies between Bretscher’s two estimates; see Table V. The cross section peaks at 5.018 b in the EDA5 analysis (an earlier EDA4 analysis is the basis for ENDF/B-VIII.0, where the resonance peak is very similar: 5.014 b).

TABLE V Location of the TD Resonance from Bretscher and French’s 1946 Los Alamos Analysis^[52,53] of Their Data Below the Resonance Energy and from Allan and Poole’s 1949 Harwell Higher-Energy Experiment^[133]*

	T Laboratory	D Laboratory	Center of Mass
Bretscher and French’s method 1 (1946)	124	82	50
Bretscher and French’s method 2 (1946)	343	229	137
Allan and Poole (1949)	155	103	62
ENDF/B-VIII.0	162	108	65

*TD resonance is in units of kilo-electron-volts. Values are given in the laboratory and c.m. frames. The energies in the triton projectile laboratory frame are a factor of 3/2 higher than in the deuteron projectile frame.

Ultimately, these Bretscher-French measurements were supplanted by the highly accurate APSST data taken at Los Alamos by Arnold et al. in 1952,^[33,34] described in Sec. V.C.7, but during the 1940s, the Bretscher-French data helped define the TN cross sections of use and informed the 1945 assessments and parameterizations in both the “Super Handbook” and Fermi’s lectures, described in more detail below. Comparisons of these parameterizations to the Bretscher-French data are also shown in Fig. 25. It is evident that Bretscher’s first 1945 data (reported in Fermi’s 1945 lectures; see below) were subsequently revised down in 1946, as also published in the 1949 Physical Review. The best assessment today, ENDF/B-VIII.0, is seen to lie between the earliest Bretscher measurements, which were too high, and the revised values that were published,^[53] which were too low.

Bretscher’s work had a swift impact on considerations of the potential for DT fusion energy production. The Los Alamos History Project, LAMD-151-1, written shortly after the war, in September 1946, says in paragraph 10.20, “In F-Division, meanwhile, new measurements of the DT cross section indicated a materially lower ignition temperature for DT mixture.”

V.C.3. The 1945 “Super Handbook”

After the completion of the Manhattan Project’s work to design and fabricate fission bombs, a conference was held to discuss the Super. The results were documented in October 1945 by Frankel et al. in the “Super Handbook,” LA-401.^[135]

The handbook gives a parameterization of the Chicago DD cross-section data (in units of barns):

(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18)

with

(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19)

where $\mathit{E}$ is the incident deuteron laboratory energy in units of mega-electron-volts.

Tables VI and VII compare this parameterization with the Chicago DDn and DDp results, which were for deuteron energies above 100 keV. The parameterization is seen to represent that data fairly well and is seen to be optimized to best fit the lowest-energy Chicago data. This choice was presumably made to improve its use in extrapolating to lower deuteron energies important in applications. The authors of the “Super Handbook” note how their parameterization for DDn was increased by a factor of about 1.35 compared with the earlier 1943 values in the Bethe-Christy handbook, LA-11,^[26] owing to reassessments of stopping powers for the thick-target experiments (see Appendix A).

TABLE VI Super Handbook^[135] DDn Parameterization Compared with Chicago Cross-Section Data by Coon et al.^[118]

Energy (Laboratory) (keV)	DDn Coon 1944^[Citation118] (b)	Parameterization^[Citation135] Eqs. (18)(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18) and (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) (b)
119	2.47E-02	2.47E-02
171	3.68E-02	3.62E-02
220	5.13E-02	4.50E-02
294	8.35E-02	5.56E-02

TABLE VII ”Super Handbook”^[135] DDp Parameterization Compared with Chicago Cross-Section Data by Coon et al.^[117]

Energy (Laboratory) (keV)	DDp Coon 1944^[Citation117] (b)	Parameterization^[Citation135] Eqs. (18)(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18) and (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) (b)
119	2.63E-02	2.63E-02
171	3.26E-02	3.70E-02
220	4.17E-02	4.20E-02
294	5.16E-02	4.32E-02

The Eq. (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) ratio parameterization shown in Table VIII is seen to match the Chicago measurements well.

TABLE VIII “Super Handbook”^[135] Ratio of DDp/DDn Parameterization Compared with Chicago Cross-Section Ratio Data and ENDF/B-VIII.0

Energy (keV)	DDp/DDn Coon 1944^[Citation114,Citation118]	Parameterization Eq. (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) ^[Citation135]	ENDF/B-VIII.0 Ratio
119	1.06	1.04	0.93
171	0.886	0.898	0.92
220	0.813	0.778	0.87
294	0.618	0.610	0.87

For the TD cross section, the “Super Handbook” reported a resonance parameterization, Eq. (20)(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20) , from Bretscher [it is equivalent to the form Bretscher presented in 1946; see Eq. (17)(17) ${\sigma }_{\mathit{DT}}(\mathit{E})=\frac{1}{E}\frac{A}{((E_r-\mathit{E}{)}^2+{\Gamma }^2)}\mathit{exp}(-1.72/\sqrt{(}\mathit{E}))\mathrm{,}$(17) , although the parameters describing the resonance there differ somewhat]:

(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20)

where the cross section ${\sigma }_{\mathit{DT}}(\mathit{E})$ is in units of barns and $\mathit{E}$ is the laboratory triton energy in units of mega-electron-volts. This functional form aimed to fit the 1943 Purdue data, as well as the preliminary TD measurements at low energy that were coming from Bretscher’s group in 1945. A functional form similar to this was presented graphically by Fermi in his 1945 lectures, as described below.

V.C.4. Fermi’s 1945 Lectures

Around the same time, before many of the Manhattan Project scientists left Los Alamos, between August 2 and October 9, 1945, Fermi gave a set of lectures on TN physics. He described studies that continued to grapple with how best to arrange a fission bomb to ignite deuterium fuel. Theoretical estimates were made of the competing energy-growth (from fusion) and energy-loss processes, often with pessimistic conclusions. Fermi ended by saying:

In concluding this series of lectures, it should be stated that they may represent a somewhat pessimistic view, in that Teller, who has been in charge of most of the work reported is inclined to be more optimistic than is the lecturer. The procedure that has been adopted to try to resolve the question of practicability of the Super is that Teller shall propose a tentative design which he considers somewhat over designed and the lecturer will try to show that it is underdesigned (that makes the pope the devil’s advocate!).

At Los Alamos, Fermi was known as the “pope of physics.” In an essay in the Biographical Memoirs of Fellows of the Royal Society, Bretscher and Cockcroft wrote,^[131]

This leadership and self-assurance gave Fermi the name of “The Pope” whose pronouncements were infallible in physics. He once said: “I can calculate anything in physics within a factor 2 on a few sheets: to get the numerical factor in front of the formula right may well take a physicist a year to calculate, but I am not interested in that.

For the DDn reaction, Fermi provided a table of cross-section values; see Table IX. Above 120 keV, the values come from the parameterization fit to the Chicago experiment. Below 40 keV, the basis for Fermi’s values is unclear to us, although at 40 keV, his 4.3-mb value is close to the 5-mb value in Bethe and Christy’s early handbook evaluation, LA-11.^[26] Fermi’s values are not so different from two sources he would have known: the “Super Handbook” parameterization [Eqs. (18)(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18) and (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) ] and Bretscher’s recently measured DDp [converted using the DDp/DDn ratio parameterization, Eq. (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) ], although it is evident that Fermi’s values tend to lie above these two sources (a factor of 2 at the lowest energy, 16 keV); see Table IX.

TABLE IX DDn Cross-Section Values from Fermi’s 1945 Lecture Listing and Other Sources from the Same Time Period Compared with Modern ENDF/B-VIII.0 Values

Energy (keV)	Fermi Lectures 1945 (b)	“Super Handbook” 1945 (b)	Bretscher Converted 1945 (b)	ENDF/B-VIII.0 2018 (b)
16	0.00025	0.00014	0.00008	0.000106
20	0.0005	0.00036	0.00023	0.0003
40	0.0043	0.0034	0.003	0.0027
120	0.02	0.025	—	0.021
300	0.05	0.056	—	0.053

It is also evident from Table IX that Fermi’s 1945 lecture has DDn cross sections that are in generally fair agreement with our best ENDF/B-VIII.0 evaluation today, becoming a factor of about 2 too high at the lowest deuteron energy, 16 keV.

The Los Alamos NSRC archives have the original laboratory notebook that Fermi and Richard Garwin shared in 1950–1951. The early pages of this notebook have Fermi’s instructions to Garwin on the background TN physics that he would need to know. We show an image of the page on DD cross sections, Fig. 26, in Fermi’s handwriting. (Garwin noted that one can tell Fermi’s text from his own because Fermi would not add a leading zero before a decimal point, as in the “A = .35” text!). The equations in Fig. 26 correspond to those in the “Super Handbook,” Eqs. (18)(18) ${\sigma }_{DD}^{tot}(\mathit{E})=(0.35/\mathit{E})exp(-1.403/\sqrt{\mathit{E}})$(18) and (19)(19) $\frac{{\sigma }_{DD}^p(\mathit{E})}{{\sigma }_{DD}^n(\mathit{E})}=1.5\mathit{exp}(-3\mathit{E})\mathrm{,}$(19) .

Fig. 26. Fermi’s Los Alamos notebook showing parameterizations of the DD cross sections.

For the TD cross section, Fermi presented a functional form graphically that anticipates the S-factor approach later used by astrophysicists, Fig. 20. His parameterization is close to Bretscher’s formula Eq. (20)(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20) presented in the “Super Handbook.” As mentioned previously, in astrophysics the cross section is represented as $\mathit{\sigma }=[\mathit{S}(\mathit{E})/\mathit{E}]exp\left(-B_G/\sqrt{(}\mathit{E})\right)$, where $\mathit{S}(\mathit{E})$ is the S-factor, which precedes the terms that vary strongly with incident energy, $B_G$ being the Gamow penetrability constant and 1/E being the factor that tracks the quantum-mechanical area from the de Broglie wavelength squared. Fermi used this approach by plotting the cross section $\mathit{\sigma }$ divided by $50exp(-1.72/\sqrt{(}\mathit{E}))/\mathit{E}$ against triton energy, which is what we would call the S-factor component (in the triton laboratory energy frame, unlike the c.m. frame typically used for the S-factor). We show Fermi’s plot in Fig. 20. It is evident that Bretscher’s 1945 preliminary low-energy TD measurements in the 20- to 30-keV triton energy range informed these fits. This Fermi lecture figure illuminates how Bretscher and French, after starting their TD measurements in July 1945, already had information on the resonant enhanced cross section by August–October 1945.

In Fig. 27, we compare Fermi’s plot of the S-factor with the Bretscher parameterization in Eq. (20)(20) $\begin{array}{rl}& {\sigma }_{\mathit{DT}}(\mathit{E})=\frac{58}{E}\frac{1}{(1+{[(\mathit{E}-0.096)/0.174]}^2)}\\ & \times exp(-1.72/\sqrt{(}\mathit{E}))\end{array}$(20) as well as that obtained from today’s ENDF, using the modern S-factor definition, Eq. (2)(2) ${\sigma }_i=S_i(E_i^{cm})\frac{1}{E_i^{cm}}\mathit{exp}\left(-\sqrt{E_i^G/E_i^{cm}}\right),$(2) .

Fig. 27. DT S-factor from Fermi’s 1945 Fig. 20 (transformed to c.m. frame) with other parameterizations from 1945–1946 and with modern ENDF/B-VIII.0 data.

Fermi’s 1945 plot, Fig. 20, appears to be the first use of an S-factor. We, and our nuclear astrophysics colleagues, have not definitively identified the first publication in the refereed literature, but it seems that it would be later than 1945. Michael Pearson, Université de Montréal, notes that “the earliest use of an S-factor I could find was by Salpeter, Phys. Rev., 88, 547 (1952),^[136] but there was no indication as to whether or not this was a first. However, for Salpeter, $\mathit{S}$ was a constant. Five years later, both Burbidge et al., “Synthesis of the Elements in Stars, Rev. Mod. Phys., 29, 547 (1957),^[137] and Cameron’s unpublished Chalk River report have an S-factor, with the difference that it is no longer a constant but is energy dependent.” Jonathan Katz, University of Washington, says, “I’m not aware of an earlier use. Most astrophysicists think reaction rates began with Burbidge et al., 1957,^[137] but that was only a review article.”

V.C.5. Los Alamos, 1946–1950

The period 1946–1950 saw many distinguished scientists and graduate students depart Los Alamos and return to their university positions, leaving Norris Bradbury with the job of rebuilding the Los Alamos Scientific Laboratory. Carson Mark was the talented leader of the Theoretical Division during much of this time. We quote his useful unclassified summary, “A Short Account of Los Alamos Theoretical Work, 1946–1950,” LA-5647-MS, written in 1974 and available from the Los Alamos library web site^[138]:

The account of the progress during this period will be given with primary reference to the theoretical work on problems of importance to the thermonuclear field.

Of course, some experimental studies (for example: cross section studies, observation of behavior of fast jets) were continued across this period and occupied, on average, the major part of the attention of something like two of the fifty or so experimental and engineering groups in the Laboratory. Such work, however, was mainly in the nature of acquiring data which were believed would be needed in connection with any attempt to estimate the behavior of a thermonuclear system. It was unlikely of itself to reduce the difficulty of undertaking a theoretical estimate, or to suggest an essentially new approach to a thermonuclear weapon. In addition, although work of an experimental and engineering kind was known to be a necessary and heavy component of any thermonuclear program, it could not rise to the high level of a full attack on the significant outstanding questions until the theoretical understanding of the processes involved in a particular system had advanced to the stage at which such questions could be isolated and clearly defined.

V.C.6. Tuck and Pimbley’s 1951 TN Data Review

In 1951, Tuck and Pimbley wrote a valuable review paper, LA-1190,^[29] which, as a practical matter, defined the evaluated cross sections that were used in simulations in 1951–1952. For many years, an unclassified version of this paper, LA-1190DEL, has been available from the Los Alamos library.

Because the charged-particle cross sections vary so rapidly with incident energy, owing to Coulomb penetrability, the researchers had moved from publishing tabulations of data to publishing simple equation parameterizations of the data with accompanying figures. (In Tuck and Pimbley’s unclassified LA-1190DEL, the DT fusion cross-section parameterization has a typographical error in it, but we cannott figure out how it is wrong.) This approach was also driven by the practical usefulness of employing parameterized values in calculations and computer code simulations. Our collections of laboratory notebooks by the researchers at Los Alamos from that era show their use of Tuck and Pimbley’s LA-1190 recommendations (e.g., Ford’s notebooks LANB 3725 and LANB 3726).

As well as recommending the best cross-section values to use, Tuck’s writings^[29] illuminate a careful assessment of the strengths and weaknesses of the measurements underpinning the data. He said, “The formal estimates given here are subject to large errors and it is necessary to assign limits to these, though we would be glad to avoid having to do this, especially as excessive caution can in this respect be as misleading as the reverse.” These are wise words, which continue to be of foremost importance for today’s ENDF cross-section evaluation “covariance” uncertainty-quantification work.

Tuck attempted to update earlier reported cross sections through use of more recently evaluated stopping powers (see Appendix A). This led to downward revisions of Bretscher’s 1945–1946 measurements, which we now know was a change in the wrong direction. By June 1951, the Los Alamos APSST experiment provided new thin-target DT cross-section data. This measurement, which we describe next, proved very accurate, agreeing with today’s ENDF data to within a few percent accuracy. Teller correctly recognized this and recommended an APSST-based cross section that was about 50% higher than Tuck and Pimbley’s LA-1190 recommendation for deuteron energies in the range 20 to 80 keV; see Fig. 28.

Fig. 28. An extract from Teller’s 1950–1951 Los Alamos lectures on TN physics. Teller correctly recommended revising upward Tuck and Pimbley’s evaluated DT cross section in LA-1190^[29] to match the new 1951 Los Alamos APSST data.^[33,34]

V.C.7. APSST, Los Alamos Advances, 1950s

The APSST experiments at Los Alamos produced accurate absolute measurements and provided the oldest data set that is still used today in modern R-matrix analyses of TN cross sections. The experiments used tritium-gas thin targets that did not suffer from the ambiguities regarding the stopping powers of thick-target materials. The data were published in a Los Alamos report in 1952^[33] and in Physical Review in 1954.^[34] The publication became well known in the fusion community as “APSST,” which as stated earlier is after its authors Arnold, Phillips, Sawyer, Stovall, and Tuck.^[34]

In an interview between Dick Garwin and Chadwick on July 20, 2021, Garwin described the role he played in 1950–1951 in motivating and developing higher-accuracy measurement of the DT and DD cross sections by James Tuck’s group at Los Alamos. From the summer of 1950 onward, Garwin came to Los Alamos as a consultant. At that point, he was a young staff member at Chicago, working with Fermi, and shared an office with Fermi during their summer visits to Los Alamos. Fermi even shared Garwin’s classified notebook to avoid having to lock up his own notebook in the safe each day!

Garwin had worked on accelerator measurements at Chicago (doing 340-MeV proton synco-cyclotron experiments) and had already become an expert in practical and engineering matters such as radio-frequency (RF) systems, electronics, cryogenics, and controlling an ion-source furnace that had been giving Tuck some trouble. For the new TN measurements in the Physics Division, he helped with RF ion sources for creating the deuterium beams, which were incident on D and T gas targets. Garwin noted that it was often remarked that “one could never get a good vacuum at Los Alamos,” owing to its high altitude. He said they were able to measure the beam energy to 10 keV and developed some clever tricks to measure differences in energy very accurately. Garwin left at the end of the summer to return to Chicago but was acknowledged in the APSST papers that reported the measurements, first in the 1952 laboratory report^[33] and later in the 1954 Physical Review.^[34]

The APSST DT data were substantially larger than Bretscher’s earlier results at the lowest energies important in applications (40% larger for c.m. energies in the 6- to 10-keV range). This finding caused some excitement, and Teller noted it in his 1951 lectures.^[37] Figure 29 shows the TD cross-section evaluations as of 1951, compared with the new APSST data. To see the rapid improvements in accuracy of the measurements and evaluations from 1943 to 1951, Fig. 30 plots ratios to the modern ENDF/B-VIII.0 values. The upper panel covers a large energy range, up to 600 keV incident triton energy, while the lower panel focuses on triton energies below 120 keV. Teller’s 1951 assessment, based on the APSST data that had just been measured, agrees very well with our best evaluation today.

Fig. 29. TD cross-section measurements by 1951. Teller quickly adopted the higher APSST measurements,^[33,34] which agree very well with today’s ENDF/B-VIII.0.

Fig. 30. TD cross-section measurements and evaluations 1943–1951 in ratio to today’s ENDF/B-VIII.0 evaluation. By 1951, the evaluations were based on the then-recent APSST data^[33,34] and agree very well with today’s values. The upper panel is for triton energies up to 600 keV, while the lower panel focuses on energies up to 120 keV.

At a conference some decades ago, Hale noted that the lowest-energy DT measurements by APSST are accurate, although at the time, the APSST authors doubted whether they could be relied upon for small cross sections that were so far below the Coulomb barrier. While the APSST Physical Review paper^[34] recommended a Gamow function analytic fit at these low energies, the earlier laboratory report^[33] contains the numerical measured data, and these are in fair agreement with our best R-matrix analyses today; see Fig. 31. For comparison, we include the later, high-accuracy Jarmie et al.,^[42,43] Brown et al.,^[44] and Brown and Jarmie^[45] measurements at Los Alamos, which especially influence the R-matrix fit. It is evident how the APSST data are more accurate, even at low energies, than the Gamow fit (horizontal line in Fig. 31). This illuminates how very accurate was this early (1952) APSST experiment, although the measurements were too low at the very lowest energies.

Fig. 31. The S-factor for the DT cross section, showing the APSST data. For comparison, we include the very accurate Los Alamos measurements by Jarmie et al.,^[42,43] Brown et al.,^[44] and Brown and Jarmie^[45] from the 1980s and 1990.

VI. FUSION REACTION RATES

The TN sigma-v-bar reaction rate is calculated as a Maxwellian average over c.m. energies $\mathit{E}$^[139]:

(21) $\overline{\mathit{\sigma v}}={\displaystyle \int }{M}_T(\mathit{E})\mathit{\sigma }(\mathit{E})v_r(\mathit{E})\mathit{dE}\mathrm{,}$(21)

with a Maxwellian distribution at temperature T:

(22) $M_T(\mathit{E})=\frac{2}{\sqrt{\mathit{\pi }}}\mathrm{.}\frac{{\mathit{E}}^{1/2}}{{(\mathit{kT})}^{3/2}}\mathit{exp}(-\mathit{E}/\mathit{kT})\mathrm{,}$(22)

and the relative speed is $\mathit{v}(\mathit{E})=\sqrt{2\mathit{E}/\mathit{m}}$, with $\mathit{m}=m_D{m}_T/(m_D+m_T)=6/5\mathit{u}$ being the reduced mass.

The evolving assessment of fusion rates has been summarized by Archer^[12] for DT and DD fusion at a variety of temperatures. Here, we provide just one temperature example: the important DT fusion rate at a temperature of 10 keV, which is a typical temperature of importance in fusion applications (e.g., NIF’s N210808 capsule experiment burned at this temperature^[1]).

As the understanding of DT fusion cross sections was improved in the 1940s and 1950s, so also was that of TN reaction rates in a hot plasma. Not only did the measurements become more accurate, but also a systematic (low) bias was removed, leading to the encouraging finding that assessments of the DT fusion rate increased substantially over time between 1943 and 1952; see Fig. 32. Tuck and Pimbley’s LA-1190 review in 1951 showed a range of values at 10 keV, varying from 0.6 to 1.4 $\times$ 10^–16 cm³/s. By the time of the accurate APSST 1952 measurement, the value had converged on our modern understanding: The ENDF/B-VIII.0 reaction rate value is 1.139 $\times$ 10^–16 cm³/s at 10 keV, which is known to about 3% accuracy. The modern assessments of the sigma-v-bar reaction rates, as a function of temperature, are shown in Fig. 6.

Fig. 32. The DT reaction rate (in units of cubic centimeters per second) at a temperature of 10 keV calculated between 1943 and 1952, compared with the modern ENDF/B-VIII.0 (ENDF8) value.

In Fig. 32, the 10-keV reaction rate from the 1943 Purdue experiment by Baker and Holloway was computed with a Gamow penetrability extrapolation and by assuming a constant resonant enhancement extrapolation below their lowest measured energy (a value of 0.4 from Fermi, Fig. 20). Bretscher’s 1946 value was based on his parameterization, Eq. (17)(17) ${\sigma }_{\mathit{DT}}(\mathit{E})=\frac{1}{E}\frac{A}{((E_r-\mathit{E}{)}^2+{\Gamma }^2)}\mathit{exp}(-1.72/\sqrt{(}\mathit{E}))\mathrm{,}$(17) . Hawkins’s history^[88] of the Manhattan Project (paragraph 5.47) describes how the Bretscher 1945–1946 data (published in Physical Review in 1949^[53]) were larger than had been anticipated based on the earlier Purdue measurements and that an assessment of the required temperature for DT burn was lowered accordingly. This was an exciting finding, and its explanation lay in the remarkable DT resonant enhancement—even at energies below the 65-keV 3/2⁺ resonance. We find that if the Purdue-extrapolated result had been correct, one would need a 15-keV plasma to create the same reaction rate as was found for Bretscher’s Los Alamos result at a temperature of 10 keV.

It is instructive to see the different energy dependencies of the three terms in the DT fusion rate equation, Eq. (21)(21) $\overline{\mathit{\sigma v}}={\displaystyle \int }{M}_T(\mathit{E})\mathit{\sigma }(\mathit{E})v_r(\mathit{E})\mathit{dE}\mathrm{,}$(21) , compared with the product of the three, the integrand, shown as a thick black line in Fig. 33. For a plasma at a temperature of 10 keV, even though the average energy of the ions is at 15 keV, the most probable energy at which fusions occur is shifted up to 40 keV. This is, of course, because of the strong energy dependence of the DT cross section and, to a lesser extent, of the average velocity.

Fig. 33. The integrand of the DT fusion reaction rate equation as a function of energy for a plasma at 10-keV temperature, as shown by the thick black line. The other three curves show the Maxwellian, the DT cross section, and the velocity (all arbitrary units).

VII. CONTROLLED FUSION ENERGY CIRCA 1946

In 1946, Bretscher et al. completed their summary report^[31] on the Super conference with a discussion on the technological advances needed to develop peaceful fusion energy applications. Their findings on controlled reactions can be found in “Peaceful Applications of the DD Reactions,” Sec. V, in LA-575-Del, available from the Los Alamos library website. They credited Barkas and Becker for proposing to use the DD reaction at low densities.

For one scheme, they discussed a dilute deuterium gas at low density, heated by electrical means. They also said, presciently, “The other difficulty is that at the low density considered, conduction losses will be extremely great and will instantaneously quench the reaction. It is hoped that by using magnetic fields one may cut down the conduction losses to the point where a continued reaction is possible, but the theory is not worked out to the point where a prediction about feasibility could be made.”

They ended cautiously, saying, “It seems that the possible use of D+D reactions as neutron sources or power producers is not yet excluded. Much more thought and some new ideas are needed. A more widespread circulation of the fundamental physics of the thermo-nuclear reaction should lead to better knowledge of its possibilities for such uses.”

Indeed, soon after this was written, in 1948–1949, the U.S. government’s classification office allowed the publication of Bretscher and French’s TD and DD Los Alamos cross-section measurements in Physical Review.^[52,55]

Van Dorn’s Ivy Mike^[140] (pp. 73–74) discusses Los Alamos scientists’ interests in peaceful fusion energy. He described a Los Alamos dinner party that he attended at Jack Clark’s house in 1952. The gathering included quite a remarkable collection of people, including Fermi, von Neumann, Teller, Bethe, Ulam, Feynman, Carson Mark (director of the Mike design team), and John Marshall. Clark called it “the gathering the LASL Super Snoopers,” and realizing an opportunity to record the event for posterity, he taped them making predictions for the nuclear age in 20 years’ time, in 1972. Unfortunately, we do not know of this tape’s whereabouts.

According to Van Dorn, on the topic of controlled fusion research, by 1972, Teller “foresaw the first convincing experiments in the control of fusion reaction energy for power production, leading to practical utilization by 1990.” Bethe, on the other hand, said, “I really do not see any prospect of producing useful energy from controlled fusion in the near future … but … I am usually wrong in such practical matters.” Bethe was the pessimist. But, a pessimist is what an optimist calls a realist.

A companion paper by Kurt Schoenberg in this special issue describes Project Sherwood research in the 1950s on controlled TN fusion.^[141]

VIII. CONCLUSIONS

By late 1942, hydrogen-isotope fusion processes had evolved from being a particular interest of Teller’s to becoming the focus of a serious research program planned for the growing U.S. nuclear science community. Our paper described the first 1930s nuclear fusion discoveries and the subsequent rapid advances in the understanding of DD and DT fusion cross sections over the decade 1942–1952.

At the 1942 Berkeley conference, Konopinski discussed the potential benefit of adding tritium to deuterium. However, we showed that Oppenheimer’s summary of the meeting instead focused on the in situ breeding of tritium within burning deuterium, after which DT reactions would occur. This was because of the scarcity of tritium and the expected large cost of its production as a TN fuel. This perspective quickly changed in the late 1940s, when reactor tritium production ramped up. For example, in 1948, Froman wrote to Los Alamos Director Bradbury saying, “The value of a neutron to form a triton is likely to become as great or greater than the value to form a plutonium atom,” and he recommended “an urgent expansion of Hanford pile facilities” to make tritium.

We have shown that Konopinski’s 1942 suggestion that the DT cross section is large was not a “mere guess” (per Teller) but, instead, was based on his knowledge of the prewar literature, probably Ruhlig’s 1938 Physical Review paper^[25] on the observation of DT neutrons created in secondary reactions following D(D,p)T, together with Rutherford’s 1937 Nature paper.^[23] Ruhlig’s strangely neglected paper should be properly appreciated as the first observation of DT fusion and the first to realize that secondary DT fusions occur in nature. We have not found any evidence from the nuclear theory knowledge of the time that they would have expected an enhanced DT (versus DD) cross section, beyond that expected from phase space due to its large $\mathit{Q}$-value, which corresponds to a factor of just 2 for DT versus DDn. Thus, it had to be Ruhlig’s experimental paper^[25,97] that inspired Konopinski and the other luminaries at Berkeley. Our appendix includes brief biographical comments on Bretscher, Tuck, Konopinski, Teller, and Ruhlig. There, we note that after Ruhlig moved to the Naval Research Laboratory (NRL), he played a part in supporting Los Alamos in the Pacific during Operation Greenhouse, where the 1951 test first created terrestrial fusion ignition.

Bethe’s suggestion that the DT cross section should be measured at Purdue and then Los Alamos led to the unexpected and remarkable 1943–1946 Manhattan Project finding that the DT cross section is about 100 times larger than DD. This transformative experimental observation brought the terrestrial production of fusion energy within the realm of the possible.

We presented images and data from historical documents in our NSRC archives, and we transcribed oral history interviews of the exciting, earliest 1943–1945 discoveries of the DT resonance-enhanced cross section at Purdue (Sec. V.B) and at Los Alamos (Sec. V.C.2)

The early, 1942–1946 measurements were accurate to about 50% or better, but by the early 1950s, the Los Alamos APSST cross sections were much more accurate, often only a few percent different from our modern ENDF/B-VIII.0 assessments (see Figs. 21 and 30). Today, the most accurate data defining our modern ENDF assessments of DT and DD fusion are the 1980s Los Alamos measurements by Jarmie and Brown.

These remarkable 1942–1952 advances in fusion nuclear cross sections (as well as Fermi’s S-factor innovation) were motivated originally by U.S. national security priorities but have enduring beneficial impacts in the basic understanding needed for peaceful controlled fusion energy and for nuclear astrophysical understanding of our human and our planet’s origins.^[4,8]

A graphical representation of the advances in nuclear fusion described in this paper is show in Fig. 34.

Fig. 34. A figure illuminating some of the main fusion advances between 1920 and 1952 described in this paper.

Acknowledgments

It is a pleasure to acknowledge useful discussions with Craig Carmer, Bill Archer, Jonathan Katz, Dick Garwin, Mike Pearson, Cameron Reed, Avery Grieve, Roberto Capote, Michael Bernardin, Alan Carr, Nic Lewis, Cameron Bates, John Moore, Richard Moore, Claudia Montanari, Petr Navratil, Daniel Odell, Carl Brune, Michael Smith, and Joyce Guzik. We particularly thank Tom Kunkle for providing historic Bush-Conant letters from the World War II OSRD archives. Thanks are due Diana Hollis, Joseph Hickey, and Jeremy Best for careful classification reviews.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under Contract [No. 89233218CNA000001]. This document was released as Los Alamos document [LA-UR-22-23373 v.4 (2022)].

Notes

^a We thank Cameron Bates for pointing us to this paper. Bates’s calculations do not support Rutherford’s explanation, though.^[24]

^b The next sentence reads “and Bretscher’s group had enough to make a target from water enriched to 25 or 50% in tritium. The water was frozen onto a plate and bombarded with deuterons.” But, here, Taschek’s memory is incorrect, for Bretscher used accelerated tritons as projectiles. It was the later APSST experiment in 1951 that used a tritium target (see Sec. V.C.7).

^c This was the common moniker for a series of three comprehensive papers on nuclear physics and resonance in the journal Reviews of Modern Physics,^[46–48] mentioned by Prof. O. Klein at the 1967 Nobel Prize ceremony^[49] awarding Bethe.

^d Resonances are characterized in the quantum theory by their properties under rotations of the three-dimensional Cartesian space. This characterization, that of the irreducible representations of the rotation group, is labeled by the angular momentum $\mathit{J}$ and parity $\mathit{\pi }=\pm 1$, discussed below. The $\mathit{J}$ is quantized in units of $\mathit{\hslash }/2$ and therefore may take values $\mathit{J}=0,\frac{1}{2},1,\frac{3}{2}$…. We follow convention by calling a resonance a “state” despite the abuse it implies to the mathematical definition of a state in quantum mechanics as a vector (ray) in Hilbert space.

^e The foundational mathematics of quantum theory is that of group theory; see Wigner’s classic book on the subject.^[58]

^f Note, however, that the isotropic angular distributions are observed for unpolarized reactants, $\mathit{d}$ and $\mathit{t}$; later, in Sec. II.C.2, we will show that the polarization reveals strong angular dependence.

^g Nuclear spectroscopic notation ${ }^{2\mathit{s}+1}{\mathrm{\ell }}_J$ uses the prepended superscript to denote number of elements in the channel spin multiplet, $2\mathit{s}+1$, where $\mathrm{\ell }$ denotes the spatial or orbital character, here the isotropic $\mathit{S}$-wave, and the appended subscript is the total spin $\mathit{J}$.

^h Employing Oppenheimer’s term, Ref. [71], p. 43.

ⁱ Compton^[30,74] noted, interestingly: “May I point out further that our appreciation of the possibilities in this direction has been made possible only by making the venture of placing this vital problem in the hands of a group of investigators, most of whom on the basis of rigid FBI test would be considered ineligible to our investigations. There are literally no other persons in the country who would’ve been able to bring this problem to a successful conclusion. Had we played safe in the sense of secrecy, we would have taken the greater risk of remaining ignorant of a powerful weapon which our enemies may use against us. Our investigations and developments are not yet complete. It is essential that we continue to be free to use our country’s best talent on this problem, even at the risk of using men who are questioned on grounds of nationality and political partisanship. It is useless to attempt to develop this program without making use of the only brains our country has that are competent to handle it.”

^j The Berkeley origins of Teller’s Classical Super are documented in the first Super patent S-680X^[82] by Teller, Oppenheimer, Konopinski, and Bethe, in which the Los Alamos lead for patents, R. C. Smith, stated in his letter to Teller of November 29, 1944: “The earliest written description which the undersigned has been able to locate on this matter is a ‘Memorandum on Nuclear Reactions’ by Dr. J. Robert Oppenheimer on August 20, 1942. It is understood that the report covers the conclusions at that time in the group of workers at Berkeley including yourself, Bethe, Serber, and the author thereof.”

^k A more complete list would be the attendees and coauthors of the Super Conference, April 18–20, 1946, LA-575, Betts, Bradbury, Bretscher, Flanders, Frankel, Frankel, Froman, Fuchs, Hamming, Hurwitz, Judd, Koller, Konopinski, Landshoff, Manley, Mark, Marvin, Metropolis, Miller, Morrison, Mullaney, Nordheim, Plaszek, Reines, Richtmyer, Serber, Teller, Tuck, Turkevich, Ulam, and von Neumann.

^l Hawkins’s 1946 Los Alamos history appears to confirm that during the July 1942 Berkeley conference, Konopinski’s guess was based on information prior to the Purdue measurements. In paragraph 5.47 of Ref. [88], the following is stated: “One further suggestion of great eventual importance was made by Konopinski. This was to lower the ignition temperature of deuterium by the admixture of artificially produced tritium (H3). The apparently very much greater reactivity of tritium led him to this proposal. It was not immediately followed up because of the obvious difficulty of manufacturing tritium and the hopefulness of igniting pure deuterium.” Unfortunately, this information is not sourced by Hawkins.

^m On June 11, 1942, Manley and Oppenheimer wrote a summary of work that was needed for the war effort, “Outline of Fast Neutron Projects,” focused almost exclusively on fission-related nuclear data needed for an atom bomb, as would be expected. DD cross sections were mentioned but only in the context of the DD neutron source reaction. The focus was on using such neutron sources to characterize fission cross sections and fission neutron spectra, not on TN fusion reactions, per se.

ⁿ For example, our calculation of a 10-μA beam with a very small 1-mm² spot size running for 100 h reproduces Ruhlig’s observation; this calculation includes a reduction by a factor of 10 owing to an estimated 90% of tritons stopping outside the regions accessible by the beam deuterons as they slow down in the target. (Note, since we wrote this, Lestone’s calculations in Ref. 97 show this possibility is much less likely, when one also considers the low possibility of the DT neutrons having enough energy to be detected in Ruhlig’s apparatus.)

^o At a later date, 1945, measurement plans for using 14-MeV neutrons from the DT source reaction were reported to Manley, in a P Division memorandum by Barschall (Nov. 7) and a group F-3 memorandum by Bretscher and Staub. Also, Hawkins’s 1947 history of the Manhattan Project^[88] (Los Alamos Project Y, Vol. II, paragraph 4.42) tells us that it was not until December 1946 that Groves gave approval for a substantial $500 000 investment for a new 8- to 12-MeV Van de Graff generator, designed by McKibben, allowing neutrons to be produced up to 20 MeV and above—“the largest generator of its kind in the world.”

^p Jonathan Katz suggested the phase-space argument to us.

^q These are charge radii. The deuteron value is from CODATA-18; the triton value is from Pohl.^[98] For the deuteron, an estimate of the matter radius of 1.958 fm by V. A. Babenko and N. M. Petrov, “Determination of the Root-Mean-Square Radius of the Deuteron from Present-Day Experimental Data on Neutron-Proton Scattering,” Phys. Atom. Nuclei, 71, 1730 (2008), is within 10% of the reported CODATA-18 charge radius, and so we do not worry about charge versus matter radius differences here.

^r This can be compared with the R-matrix EDA code value that we use for the total d+t radius, which is 5.1 fm, which is not far from the 4.9-fm value shown here. The d+d radius is substantially larger, 7.0 fm. This has a somewhat different meaning in R-matrix theory from the charge radius or mass radius of the interacting nuclei, and it is the separation at which there are no effective interactions between the d and t nuclei other than Coulomb.

^s Bill Archer’s excellent paper, “A History of Boost,”^[12] indicated that this document was lost. One of us (MBC) found it, hidden in plain sight within the S-680X patent documentation in the context of Ref. [79], Oppenheimer’s “Memorandum on Nuclear Reactions.” To whom Oppenheimer’s memorandum was sent is not known, but we think it would have been sent to leaders such as Compton, Bush, Conant, and Groves. Oppenheimer’s memorandum addresses only the H-bomb. Presumably, a similar document was created on fission bomb feasibility, but we do not have a copy (except for a November 1942 Oppenheimer-Peierls letter^[102]). It would have been sent by Oppenheimer to the OSRD. Other sources indicate that the group at Berkeley was also confident regarding the feasibility of a fission bomb.

^t Archer^[12] cites this same patent as the earliest documentation of the concept of boost.

^u James Chadwick took over as liaison officer when the British effort moved to America. General Groves played a role in Akers being removed. Akers was associated with Imperial Chemical Industries and with the possible postwar commercial exploitation of nuclear energy. On November 2, 1943, Groves reported to Conant that he had been asked “whether we had any specific objection to Akers; whether we thought him incompetent or impossible to get along with. I told him that in general I just liked Chadwick better to deal with and that I always felt a little on my guard in talking with Akers just as I do in talking to our own industrialists and that I do not have that feeling about Chadwick.” He also said, “We feel quite strongly that it was generally understood that Akers would be eliminated from the picture….We think it is a splendid idea to have him out.” Great stuff.

^v Reference [90] cites this as “R.E. Schreiber, private communication to S. Gartenhaus, June 1996.”

APPENDIX A

STOPPING POWERS TO INFER CROSS SECTIONS

Early DD and TD cross-section measurements were made with thick targets, before thin-target experiments were perfected. Such experiments measured the thick-target neutron production for a range of increasing projectile energies incident on heavy water ice, D₂O, and on other deuterated compounds. As the proton beam slows down, nuclear reactions occur at different proton energies. If the stopping power is known as a function of incident energy, one can infer the cross section as a function of incident energy.

The first hydrogen-ion stopping power measurements were by Gerthsen, Eckardt, Reusse, and collaborators at the University of Tubingen and Kiel University, around 1930. These studies provided energy loss for slow protons on various media, including hydrogen, air, and celluloid. Around the same time, Bethe, in Munich, developed the theory of how charged particles slow down and his formulas for the phenomenon. These 1930s German assessments of stopping powers for protons were adapted to provide D and T stopping power assessments for the 1940s U.S. thermonuclear measurements at Chicago, Purdue, and Los Alamos.

Various assumptions were made by the U.S. authors, who needed stopping powers for D and for T ions incident on D (heavy water) targets:

1. The rates of energy loss (stopping powers) for protons, deuterons, and tritons are the same for ions of the same velocity, so, for example, a 10-keV proton, 20-keV deuteron, and 30-keV triton have the same stopping powers.

2. The atomic stopping powers of p and d targets are the same (so heavy water is the same as light water, per molecule).

3. The molecular stopping power of D₂O can be obtained by summing the stopping powers of two atoms of D and one of O.

4. The stopping power is independent of the physical state: liquid water or solid ice.

As the stopping powers were reassessed using additional data and theoretical considerations, the TN cross-section assessments were revised in the mid-1940s and 1950s. At Los Alamos, on September 23, 1943, 6 months after scientists started arriving at Los Alamos for the Manhattan Project, an assessment was made by Ashkin, Bethe, and Weisskopf, in LA-12-R, with a focus on the lower energies that were needed (deuterons below 100 keV). These were subsequently revised by Los Alamos scientists in the TN measurement group F-3. French and Seidl provided an assessment in LA-392, in June 1946, which was the basis for the Bretscher and French DD and TD measurements reported in 1946 and published in Physical Review in 1948 and 1949.^[126,127]

The degree of the validity of these four assumptions was much discussed by the Los Alamos authors, based on both early experimental works and theoretical consideration. They were thought to be good, and today, they still appear to be fairly good assumptions.

There is some evidence that the stopping powers of liquid and solid water are different at very low energies [see, for example, figures available at the International Atomic Energy Agency (IAEA) Nuclear Data Section’s website on stopping powers, https://www-nds.iaea.org/stopping-legacy/stopping_201604/stopping_timg.html]. D. A. Andrews and G. Newton^[142] endeavored to use the (by then) known DT cross section to infer the stopping powers of deuterons on heavy ice, at Harwell, and they observed substantially lower stopping powers between 5- and 20-keV equivalent proton energy, versus, say, International Commission on Radiation Units and Measurements Report 49 (ICRU49), “Stopping Power and Ranges for Protons and Alpha Particles,” liquid water, per a figure provided to us by Claudia Montanari, an IAEA consultant.

Tuck and Pimbley reviewed all these assessments in their seminal April 1951 review, “The DD and TD Cross Sections,” LA-1190. They provided their own reassessments of the D and T stopping powers for heavy water, leading them to reassess (down) the earlier Bretscher and French cross sections, and these reassessed values were the basis of their analytic parameterizations. Unfortunately, with hindsight, their reassessed stopping powers were too low, leading to cross-section recommendations that were too low. This mistake was soon appreciated. The high-accuracy APSST thick-target TD measurement^[33,34] at Los Alamos came in June 1951, leading Teller to point out that the true TD cross section is substantially higher; see Fig. 28.

Fig. A.1. A reproduction of Tuck and Pimbley’s Fig. 12 in LA-1190, showing the stopping power of deuterons on D₂O molecules. For comparison, we show modern values from ICRU49 evaluated tables (which come from NIST’s PSTAR) and MNCP6 inline calculations. The ICRU49 values are more accurate here.

Figure A.1 reproduces Tuck and Pimbley’s Fig. 12 from their review of stopping powers in LA-1190. In this useful figure for deuterons incident on D₂O, Tuck and Pimbley use the convenient stopping power units of (eV/cm) per (molecule/cm³). To show stopping powers in these units, they need to be converted from the standard units used at the time, which was (keV/cm) in water vapor at 15-mm mercury pressure at room temperature, 15°C (which is a little cold by modern standards!). Under this condition, 1 cm³ contains 1.1 g D₂O. This allows for the conversion of the tabulations by Ashkin et al. and French et al. into the units used by Tuck and Pimbley. An example is given in Table A.I for French’s LA-392 data. We note that French’s erratum in Physical Review, 73, 1474 (1948), says his numbers should be scaled down by 10% because he now assesses low stopping powers based on Crenshaw data.

TABLE A.I Stopping Powers in Heavy Water (Ice) from French and Seidl’s 1946 LA-392

$E_P$(keV)	$E_D$(keV)	LA-392 (keV/cm) 15 mm Hg, 15℃	LA-392 (eV/cm) /D2O/(cm^Citation3)
5	10	0.29	8.7E-15
10	20	0.43	1.3E-14
15	30	0.55	1.6E-14
20	40	0.72	2.1E-14
25	50	0.78	2.3E-14
30	60	0.84	2.5E-14
35	70	0.89	2.7E-14
40	80	0.94	2.8E-14
45	90	0.98	2.9E-14
50	100	1.03	3.1E-14

TABLE A.II Stopping Powers in Heavy Water (Ice), in Tuck and Pimbley’s Units of eV/cm per D₂O molecule/cm³, from French and Seidl’s 1946 LA-392, Compared with Values Adapted from ICRU49 (= NIST’s PSTAR) and MCNP’s Default Calculation

$E_P$(keV)	$E_D$(keV)	LA-392	ICRU49 = PSTAR	MCNP
5	10	9	9	12
10	20	13	13	17
15	30	16	15	20
20	40	21	17	22
25	50	23	19	24
30	60	25	20	25
40	80	28	22	27
50	100	31	23	27

Today, some of the best recommended stopping powers come from the National Institute of Standards and Technology’s (NIST’s) PSTAR evaluation, as adopted by the ICRU49 and International Commission of Radiation Units and Measurements Report 90, “Key Data for Ionizing-Radiation Dosimetry: Measurement Standards and Applications.” However, even today, the best estimates of stopping powers at low energies are quite uncertain; below 100-keV proton energy, ICRU49 estimates 5–10% uncertainties. Table A.II provides a comparison of stopping ranging from the early, 1940s LA-392 values to modern values from ICRU49 and MCNP (which uses an inline formula and is not expected to be more accurate than ICRU49, here). These modern values are added as blue and red points on Tuck and Pimbley’s old figure in Fig. A.1.

The old, 1946 LA-392 stopping power data (and French’s revisions) are seen to agree well with modern ICRU49 values at the lowest energies (below deuteron energies of 30 keV) but are too high for deuteron energies of 40 to 100 keV (and in fact agree with MCNP, here).

APPENDIX B

DRAMATIS PERSONAE

B.I. Egon Bretscher

As the leader of the earliest TD and DD TN cross-section experiments at Los Alamos, 1944–1946, Bretscher plays a central role in this paper. He was not the first to measure the TD cross section and observe its large resonant value—that was Baker and Holloway at Purdue in 1943 for the Manhattan Project—but Bretscher was the first to measure TD at low triton energies (in the tens of kilo-electron-volt range) that are important for TN applications. He was also the first to write on the likely cause of the large cross section,^[52] which is a resonance in the A = 5 system, although Bethe and others must have discussed this following the earlier Purdue experiments (see Sec. V.B). Figure B.1 shows Bretscher at the San Ildefonso Pueblo, New Mexico, in 1946.

Bretscher had moved from Switzerland to Rutherford’s Cambridge laboratory in 1936, performing pioneering measurements on neutron fission.^[9] As discussed in our previous paper,^[9] Bretscher realized in 1940^[143] that the to-be-discovered ²³⁹Pu element would have favorable properties for a fission bomb, which is an insight also independently made in the United States around the same time or slightly earlier. Bretscher and Feather are traditionally credited^[121] with the first U.K. insights into the potential usefulness of ²³⁹Pu. Mark Bretscher, Egon’s son, told MBC that it was sadly a cause of much unhappiness in the Bretscher family that this insight was credited to Feather as well as Bretscher. Mrs. Hanni Bretscher wrote^[144] in 1961 to the historian Margaret Gowing that “Feather’s name got attached to this 94 work through his own insistence, he justified by ‘having shouldered the burden of administration for the group.’ My husband was probably too soft hearted in this matter.” Hanni (Fig. B.2) went on to challenge Prof. Smyth, writing to him that “My husband was the first here to foresee the possibilities of plutonium” and noting that this British contribution was not properly included in the 1945 first edition of Smyth’s famous report, Atomic Energy for Military Purposes. In 1961 correspondence between Hanni Bretscher and Gowing, she describes^[144] how she was a witness to the British scientist Kemmer’s suggestion of the name “plutonium,” since other actinides were named after the planets, a name independently proposed by the American scientists. She also notes that scientists on both sides of the Atlantic made the same etymological mistake “as plutium would surely be the correct name.” She went on, writing humorously, that “I am ashamed of having being present at the birth of the wrong name.” (Frank Close’s book on the Higgs discovery discusses Kemmer in some detail.^[145]) Seaborg has described his reasons for choosing the name plutonium instead of plutium: He just preferred the way it sounded.

Gowing^[121] described the discussions in 1943 among Chadwick, Peierls, Groves, and Oppenheimer (p. 161), regarding Chadwick’s British team who would move to Los Alamos, “It was agreed that he should bring to Y a group of his best experimental physicists, Frisch, Rotblat, Bretscher and Titterton, for example.” At Los Alamos, Bretscher led Group F-3 in Fermi’s Division, charged with measuring TD and DD cross sections with his student, Anthony French. Section V.C.2 describes the results they obtained.

After the war, Bretscher was unhappy with Cambridge’s Cavendish Laboratory director Lawrence Bragg (who succeeded Rutherford) because of new directions being set away from nuclear physics. In March 1946, Bretscher wrote to his friend Sam Allison of the Chicago Met Lab: “I am so wild about Bragg and his tricks, that I have sent in my resignation to Cambridge. Chadwick, whom I am also going to see, agrees with me completely. To hell with this English Gentleman Bragg.”^[144] So, instead, in 1947, Bretscher moved to Britain’s Atomic Energy Research Establishment at Harwell, as head of the Chemistry Division. After Otto Frisch vacated the position of head of the Nuclear Physics Division at Harwell to move to Cambridge, Bretscher took up that role for almost 20 years. He was appointed a Commander of the Order of the British Empire^[146] on his retirement from Harwell.

Fig. B.1. Egon Bretscher at the San Ildefonso Pueblo, New Mexico, January 1946. (Courtesy Churchill Archives Center, Cambridge University.)

Mark Bretscher, Fellow of the Royal Society, kindly wrote for us a biographical sketch of his father. (Mark was a child in Los Alamos during the Manhattan Project.) He describes his father’s work at Harwell after the war:

Most scientists at the UK’s Atomic Energy Research Establishment (AERE) lived off site, but not my parents. Frequently Egon would invite 2–3 members of staff and visitors to coffee after lunch where they would chat for around an hour; in this way, us children met many of these during school holidays and gained the impression that these occasions were often highly entertaining. He was pretty withdrawn, coming home in the evening from work, tired, usually disappearing into his study and reappearing at supper. And not much conversation at supper—very little politics. After that, he would retire to our sitting room, smoke a cigar sometimes and play the piano, a Bechstein Grand (made in 1892). And so, as I used to go to sleep, my father’s playing wafted upstairs and I loved listening. Chopin, Bach, and other wonderful pieces. He was a good pianist. Over the weekends, he and I often went for a walk around the “fence,” the perimeter of AERE built on the old air strip.

He and my mother loved the south of Switzerland (Ticino) and bought a parcel of land and built a holiday house there, just above the Lago Maggiore, and to which we went each summer for about 6 weeks, although Egon only stayed for maybe a couple of weeks. Various friends came and visited us there—including the Staubs and Blochs.

There is no doubt that, having watched the Trinity explosion and then film footage of the aftermath in Hiroshima and Nagasaki, my father was deeply troubled: I am sure that changed his character. He spent many sleepless nights my mother told me. As such, he never talked about his science to us. But, around 1956/7, I was asked to give a talk at Abingdon school about nuclear energy. My father opened up—and this was the only occasion he did so, explaining isotopes, piles, bombs, the Windscale accident and the Wigner effect. It provided a great talk. And a happy memory.

My brother Peter reminded me of our father’s passion for saving earth worms: at Harwell, after a good rain, these creatures were frequently seen trapped on the roads. Egon, on his way to the lab, would dismount from his bicycle (he never drove), pick up the worm and transfer it to a grassy area. We thought this might be a reaction to his contributions to the A-bomb.

He loved walking—at Los Alamos he went for hikes with other scientists—I believe particularly with Teller. He was quite a good mountaineer and once bragged that his greatest contribution to science was to save Felix Bloch’s life: the two (students in Zurich) were coming down a glacier when Felix, roped to my father, fell over a cliff edge. My father very swiftly managed to get his ice ax into the ice and hold them both. He managed to lower Felix, who had broken a leg bone, onto a ledge, then climbed down to tie him onto the ledge. Egon then went down to raise help and came back and a rescue team eventually brought Felix down.

Mark Bretscher added that Mark Oliphant was a close friend to his parents and played with him in the early 1940s. It was arranged with Oliphant that should his parents perish in the war, Oliphant would adopt Mark.

More on Staub and Bloch at Los Alamos can be found in a paper on their Manhattan Project prompt fission spectrum measurements.^[147]

B.II. James Tuck

Tuck was another British émigré to the United States, who first came to Los Alamos as part of the Manhattan Project and returned a few years later, becoming the Physics Division’s associate division leader through 1973. Moore and Brown described aspects of Tuck’s 1944–1945 work on shaped-charge high-explosive lenses in their recent paper for the Manhattan Project in the ANS Nuclear Technology special issue.^[123] The present paper, instead, focuses on Tuck’s APSST cross-section work in the early 1950s, described in Secs. V.C.6 and V.C.7.

When Teller described his first fusion discussion with Fermi at Columbia University, 1941, he said^[148] that this was “before the British great help arrived” to the Manhattan Project. Tuck was a co-inventor of the high-explosive lens system used in the Fat Man implosion device. When discussing the spring 1946 Super conference held in Los Alamos, Teller highlighted “two men very interested in TN development and each made his mark—Richtmyer, and Jim Tuck, from Britain.” Indeed, the October 1945 “Super Handbook,” LA-401,^[135] documenting the proceedings from a Los Alamos meeting toward the end of the Manhattan Project, provided the last formal assessment of TN cross sections prior to Tuck and Pimbley’s 1951 LA-1190 TN cross-section review.^[29]

Dick Garwin talked with us about Tuck during an interview in 2022, since Garwin and Fermi provided technical advice on the seminal APSST DT cross-section experiment that Tuck and colleagues performed in 1951 (see Sec. V.C.7). Garwin described to us how Bradbury and Kellogg (the Physics Division leader) recruited Tuck back to Los Alamos in 1949 but had him work at Chicago for a while until his security clearance came through. Teller described how “Tuck had shelved his great interest, peacetime applications of atomic energy, and devoted himself to the urgent phase of the program,”^[83] referring to the urgency in the United States to develop an H-bomb following the Soviet’s first nuclear test, in 1949. A companion paper by Kurt Schoenberg in this special issue describes Tuck’s Los Alamos research in the 1950s on controlled TN fusion,^[141] for Project Sherwood.

B.III. Emil Konopinski

Konopinski was a researcher at Chicago before joining the Manhattan Project. Together with Berkeley, Chicago was the place to be, as the center of gravity of the U.S. top researchers in nuclear science. Konopinski worked closely with Teller and Fermi and joined the group of researchers who came to Los Alamos for the Manhattan Project. He is credited for the key insight, at the July 1942 Berkeley conference organized by Oppenheimer, that the DT cross section would be advantageous for use in fusion (Sec. IV.A.1). Teller called this an “inspired guess,” but this paper has shown that Konopinski knew of prewar work suggesting that the DT reaction rate is large; see Sec. IV.A.2. Reference [84] provides an audio clip of Konopinski saying this.

At Los Alamos, Konopinski worked out many of the underlying theoretical physics formalisms for fusion burn and radiation transport. Later, he became known for his theoretical research in light-particle scattering theory and in the theory of beta decay. An oral history interview with Konopinski in the NSRC archives provides interesting listening. One anecdote in that interview, on the differences at Los Alamos between U.S. scientific staff and immigrants from Europe, is noteworthy. Konopinski indicated that the U.S. researchers tended to be egalitarian, with nobody worrying about reporting to a talented group leader who happened to be younger than them. The European scientific immigrants, on the other hand, tended to be concerned about such matters and were continually worried about their status.

Teller had a high regard for Konopinski, saying of his contributions on Super research during the Manhattan Project, “The most important part of all this work, however, was focused on one man, Konopinski. It was he who brought newcomers up to date…and who made sure that our accumulating knowledge was preserved in clear and usable documents.” Teller also credits Konopinski for working with him in 1942 (following Fermi’s first 1941 suggestion) to show that deuterium could in principle be used in a TN bomb and for proving “that the Super bomb could not ignite the atmosphere or the ocean.”^[83]

B.IV. Edward Teller

Any biographical comments on Teller seem superfluous, given the extensive literature describing his career and personality. But, in the context of this paper, a few words are still warranted. Having had the benefit of reviewing the Los Alamos NSRC archives that contain Teller’s technical writings from the 1940s and early 1950s, it is noteworthy how remarkable these writings are. His physics reports are extensive, clear, and didactic, and his handwritten notebooks are equally so. It is also evident that this was a man who was driven by an overriding passion for bringing the H-bomb to fruition, always expressing confidence that it could be done. At times, it might have seemed against the odds, but he eventually succeeded in this decadal quest,^[149–151] between 1941 and 1952, when Los Alamos executed the successful Ivy Mike test.

From this earlier period of the 1940s, coworkers would speak very positively of Teller. In an interview with one of us (MBC), Garwin noted his “warm personality, and how he loved talking physics.” Admittedly, though, after describing how he saw Teller walk out of a high-level meeting in Los Alamos, in September 1951 (when the laboratory director Bradbury announced that Marshall Holloway, not Teller, would be leading the engineering and manufacture of the Mike device), Garwin said, “He had been unhappy since 1943.” Photographs of Teller often show him in later years, with his walking staff and his overgrown eyebrows. Figure B.2, instead, shows him in the summer of 1946, on a hike with the Bretscher family, climbing Lake Peak in the Sangre de Cristo mountains to the northeast of Santa Fe.

Fig. B.2. Teller, photographed by Egon Bretscher, pictured with Bretscher’s wife, Hanni, hiking Lake Peak near Santa Fe, New Mexico, 1946. (Courtesy Churchill Archives Center, Cambridge University.)

B.V. Arthur Ruhlig

Arthur (Art) J. Ruhlig was born in the Detroit suburb of Wayne, Michigan, on June 13, 1912, to Otto and Susan (née Sell) Ruhlig. He married Emily Alverna Taisey; they had three children. He was a student of Horace Richard (Dick) Crane in the graduate program of the Department of Physics at Michigan. He began graduate work in 1933 and was awarded a doctorate degree in January of 1938 for the study of “The Passage of Fast Electrons and Positrons Through Lead.” He published a strangely neglected letter—given its import for the potential of terrestrial fusion—titled, “Search for Gamma-Rays from the Deuteron-Deuteron Reaction” in Physical Review, dated August 1, 1938,^[25] in which he adjudged the reaction D(T,n)α to be “exceedingly probable.” This judgment was based on a quantitative estimate of this reaction’s rate relative to deuteron-deuteron reactions. His career took him to industry after this postgraduate work, and in 1952, he was at the Naval Research Office in Washington, D.C. In 1960, he was named manager of physics and computing at the Aeronutronic Division of the Ford Motor Company in Newport Beach, California, and in 1964, he was working as technical staff at Philco Research Laboratories in Newport Beach. He passed on July 26, 2003, in Santa Ana, California.

We have located a 1936 photograph that includes Ruhlig from the Eastern Kentucky University archives; see Fig. B.3. The scientists shown in the photograph are a group at the Nuclear Symposium at Michigan. Pictured are E. O. Lawrence, P. P. Ewald, J. D. Kraus, Baldwin R. Curtis, E. L. Harrington, Catherine Chamberlain, Richard W. Quarles, David M. Dennison, L. W. Nordheim, Zaka Slawsky, I. Rabi, Milton Slawsky, Gertrude Nordheim, Lucy H. Kurrelmeyer, Hugh C. Wolfe, Miss His-yin Sheng, E. U. Condon, J. M. Cork, H. A. Bethe, S. A. Goudsmit, G. Breit, Paul Rood, M. E. Rose, James Perdue, J. R. Lawson, William Rarita, C. E. Rood, Thomas J. Carroll, Fern Trovillo, Siiri Markkanen, Jenny Rosenthal, C. E. Ireland, Rose C. L. Mooney, Donald S. Bayley, H. H. Siemers, Donald G. Hurst, J. E. Hill, Melba Phillips, A. J. Ruhlig, John Bardeen, Otto Laporte, M. H. Hebb, E. W. Uehling, C. D. Hause, O. G. Koppius, R. D. Present, Bernard Kurrelmeyer, W. H. Furry, V. E. Bottom, Eugene Feenburg, Claude Cleeton, Joseph M. Keller, David Inglis, Charles T. Zahn, E. L. Hill, Martha Cox, Harold Lifschutz, James H. Bartlett Jr., Miss I-djen Ho, Edward S. Akeley, W. W. Sleator, R. A. Boyd, Gordon M. Shrum, J. S. Koehler, J. G. Black, Daniel L. Rich, A. H. Spees, R. L. Thornton, A. W. Smith, Jonathan Parsons, and D. B. McNeill. It is unclear which is Ruhlig; we leave that as an exercise for the reader! If any readers know of a photograph of Ruhlig, please let us know.

As part of the NRL team supporting the Los Alamos 1951 Operation Greenhouse tests in the Pacific, Ruhlig led a diagnostic group responsible for amplifiers and transmission lines. It seems appropriate that having been the first to observe DT fusion in 1938, Ruhlig was part of the team that first observed an ignited burning fusion plasma in the first thermonuclear test explosion. Documentation for these tests can be found in the online vault (OLV) at Los Alamos; see document WT-96, “Operation Greenhouse: Scientific Director’s Report of Atomic Weapons Tests at Eniwetok, 1951,” and NRL documents NRL-3974 and NRL-3975. A formula developed by Ruhlig published in “The Energy Spectrum of the Productions of a Thermal Reaction,” NRL-3775 (1950), to infer the temperature of a burning plasma from the observed neutron spectrum, has been widely used over the decades, as can be seen in documents on the OLV following a search on “Ruhlig.”

Fig. B.3. A group at the Nuclear Symposium at Michigan, 1936, including Ruhlig. Digital Collections, accessed September 30, 2023, https://digitalcollections.eku.edu/items/show/3347. (Credit: Eastern Kentucky University, with citation per their guidance.)

APPENDIX C

LOS ALAMOS NUCLEAR PHYSICS CONFERENCE 1946

Figure C.1 shows the agenda of the August 19–24, 1946, conference at which the photograph in Fig. 3 was taken. The event is recorded in Truslow and Smith, “Manhattan District History – Project Y – The Los Alamos Project – Vol II – August 1945 through December 1946,” pp. 205–206.

In documentation held in our NSRC archives, Bradbury explained that the purpose of this conference was to bring together scientific leaders to provide useful advice to the laboratory regarding future directions. Many of the invitees had been at Los Alamos during the war, but some had not. Bradbury also wanted this conference to be on less-sensitive, nonweapons topics, and TN cross sections were not on the agenda because the DT and DD cross sections were still classified in 1946. Relevant to this paper, though, Wigner gave a talk on resonances. This was just a year before the publication of his famous paper with Eisenbud on R-matrix theory.

Fig. C.1. Agenda for the nuclear physics conference, Los Alamos, August 1946.