Some of the History Surrounding the Oliphant et al. Discovery of dd Fusion and an Inference of the d(d,p)t Cross Section from This 1934 Paper

Abstract

A review of the flurry of papers involving deuteron beams in 1933 and 1934 reveals some aspects of historical significance. A team led by Lawrence saw several mega-electron-volt protons and neutrons from deuteron-plus-deuteron (dd) fusion in 1933 before the discovery of this process by Oliphant et al. in 1934. However, Lawrence et al. failed to notice deuteron contamination in their targets, and instead incorrectly concluded that the protons and neutrons were being emitted back to back from the breakup of the deuterons in the relevant center-of-mass frame. By observing disintegrations induced by deuteron beams incident on deuterated targets, Oliphant et al. correctly identified dd fusion proceeding through an intermediate excited ⁴He nucleus that broke up into either back-to-back protons and tritons or back-to-back neutrons and ³He nuclei.

Here we use Oliphant et al.’s proton production rates to infer d(d,p) cross sections that are twice the known modern values. This discrepancy is likely due to our lack of knowledge of some key aspects of Oliphant et al.’s 1934 experimental setup. However, the deuterium beam energy dependence of Oliphant et al.’s d(d,p) proton production rate is clearly consistent with the quantum mechanical tunneling through the Coulomb barrier associated with the fusion of two hydrogen isotopes.

Keywords:

• Fusion
• deuterium
• Oliphant

I. INTRODUCTION

After the discovery of “A Hydrogen Isotope of Mass 2” by Urey et al.^[1] in 1932, deuteron beams quickly became “the new club to attack the nuclear enemy.”^[2] A flurry of work on nuclear disintegration involving deuterons in 1933 and 1934^[3–9] climaxed with the observation of deuteron-plus-deuteron (dd) fusion by Oliphant, Harteck, and Rutherford.^[3] This was one of the great discoveries of the twentieth century. Even though the community at that time was leaning toward the deuteron being “a proton and a neutron closely combined,”^[7] ideas that it could be a primary noncomposite object or a composite consisting of two protons and an electron still persisted.

Lawrence et al.’s^[4,5] observations of deuteron interactions with an array of targets led them to suggest that “the deuton itself was disintegrated as a result of nuclear collisions … .” This supported the idea that the deuteron was a composite object containing both a proton and a neutron. However, Lawrence et al. went further, suggesting that deuterons could break up into a proton and neutron in the field of target nuclei with no transformation of the target nucleus. With the now-known deuteron binding energy of 2.2 MeV, we know that Lawrence et al.’s suggestion (at the relevant energies) violates conservation of energy, and is thus incorrect. However, at the time, with the true mass of the neutron considered by some to be an open question, the nature of the apparent breakup of the deuteron in Lawrence et al.’s 1933 experiments would have been possible only if the neutron mass was ~1.0006^[4,5] atomic mass unit (amu) instead of the value of 1.0067 obtained by Chadwick.^[10] The modern value is 1.008665 amu.

The back-to-back disintegration of the deuteron nicely explained why the proton and neutron emissions were of equal intensity and similar energies. However, the lowering of the neutron mass would have had “profound theoretical implications,”^[5] including some novel properties for the deuteron. Rutherford summarized the situation toward the end of 1933 saying, “On Lawrence’s view, the diplon is a nucleus of an unusual type, for it possesses about 5 million volts of excess energy, which can be released under appropriate conditions.”

Four papers from the Cavendish in 1933 and 1934^[3,6–8] appear to have been initiated and/or justified in part by the deuteron suggestions of Lawrence et al.^[4,5] The first, by Oliphant, Kinsey, and Rutherford,^[6] studied disintegrations involving separate deuteron and proton beams on separated ⁶Li and ⁷Li targets. The second was by Rutherford and Kempton^[7] who studied the interaction of alpha particles with heavy water. Neither of these Cavendish studies saw any deuteron breakups that might have been expected given the interpretation of Lawrence et al.^[4,5]

Following the previously mentioned Cavendish experiments,^[6,7] Oliphant et al.^[3] embarked on a program to attempt the observation of protons from interactions of a pure deuteron beam on several deuterated targets. Based on the early work,^[6,7] they were expecting very low count rates, and they made multiple changes to a previous experimental setup^[11] to significantly increase the rate of the observed disintegrations. However, Oliphant et al.^[3] reported they were “… surprised to find that on bombarding heavy hydrogen with diplons an enormous effect was produced.” From their experimental observations, they correctly inferred the d(d,p)t and d(d,n)³He channels, and in doing so discovered the A = 3 isotope of hydrogen, i.e., the triton.

The energy of the outgoing protons and tritons was used to infer a triton mass of 3.0151 amu (the modern value is 3.0155). They estimated the energy of the d(d,n) neutrons to be ~2 MeV (the modern value is 2.45 MeV). This confirmed, within their experimental uncertainties, the neutron mass obtained by Chadwick.^[10]

They^[3] also observed that the dd fusion protons and neutrons were generated at nearly equal rates. One of the differences between the experiment of Oliphant et al.^[3] and Lawrence et al.^[4] was that in Oliphant et al.’s apparatus, they could see the short-ranged ³He ions that accompanied the protons. The correctness of the back-to-back nature of the proton and triton emissions in the relevant center-of-mass frame was soon verified by Dee.^[8]

Given our present understanding of the monumental nature of the discovery of hydrogen isotope fusion by Oliphant et al.^[3] it is of some interest to note that they did not use the word “fusion” or speculate about terrestrial and astrophysical nuclear energy possibilities, of which they must have been aware given Eddington’s breakthrough insights in his 1920 paper.^[12] Instead, they dryly reported their observations and made conclusions about the relevant nuclear reactions. From my reading, their only hint of any possible excitement was

… [T]he neutrons resulting from the bombardment of diplogen with diplogen are homogeneous in velocity, and since large yields are obtainable at comparatively low bombarding potentials they should serve as an almost ideal group for experimental work on the properties of neutrons.

Indeed the d(d,n) reaction quickly became a key neutron source for nuclear reaction studies.

Oliphant et al.^[3] also explained that only an exceedingly thin layer of their targets contributed to the deuteron-on-deuteron activity and “[c]onseqently every substance we have bombarded with diplons begins, after a short time, to show effects which are clearly due to traces of diplogen absorbed by or driven into the target.” This statement can be interpreted as Oliphant et al.^[3] politely informing the readers that Lawrence et al.’s 1933 targets would have become deuterated and a source of dd fusion neutrons and protons.

In light of this, we have since come to understand that many targets exposed to a fast deuteron beam will yield d(d,p)t and d(d,n)³He reactions, and it is known^[2,9] that Lawrence et al.^[4,5] were, in fact, observing dd fusion protons and neutrons in 1933. It thus appears that if Lawrence was not so willing to dismiss the neutron mass obtained by Chadwick,^[10] and had refrained from publishing until they further investigated their interesting and important experimental findings, then Lawrence et al. may well have been the first to discover dd fusion.

Despite it being known that Lawrence’s incorrect claim of deuteron disintegration in 1933 likely caused him to miss out on the discovery of dd fusion, this appears to have not been directly discussed in the nuclear physics peer-reviewed literature. Instead, the papers of others focused more on why Lawrence’s claim of deuteron disintegrations should be dismissed, but did not directly point out that Lawrence was seeing protons and neutrons from dd fusion in 1933.

For example, Tuve and Hafstad,^[9] who essentially repeated the Berkeley experiments in 1934, stated, “There is thus no evidence in these observations to support the Berkeley suggestion of a neutron-mass lower than that given by Chadwick.” They also concluded “that deuterium (from the beam) is the contamination responsible for the proton-group …” observed by Lawrence. However, they stopped short of stating that what Lawrence interpreted to be the disintegration of deuterons was in fact dd fusion, despite the clear inference that all interested parties must have been making.

In a private communication, Oliphant broke the news gently^[2] to Lawrence stating, “We suggest very tentatively that your results may be explained as due to the bombardment of films of D and of D compounds … . I hope these results are of interest to you.” Historians have been less kind. Heibron and Seidel,^[2] in regard to events surrounding the 1933 to 1934 timeframe stated, “The persistence of the Laboratory (Berkeley) in its error spread its reputation for sloppiness and forced others to make an important discovery.” Our musings on the discovery of dd fusion help remind us that many great discoveries are preceded by serendipitous events and are often preceded by a period of confusion.

II. SIMPLE THEORY OF dd FUSION CROSS SECTIONS

In the first few years after the invention of new particle accelerators in the 1930s,^[13,14] many authors tended to focus on experiments that might reveal new phenomena, establish the relevant reaction mechanisms of these new phenomena, and yield reaction Q-values. The careful measurement of absolute production rates and/or the inferences of reaction cross sections often had to wait until the importance of a new process was established.

The discovery of dd fusion followed this common trend. After the realization of applications in the 1940s,^[15] the reporting of dd-fusion cross sections became more commonplace, with increasing levels of experimental complexity and accuracy obtained over time. When evaluating fusion cross sections in the late 1930s and 1940s, it was convenient to express them by the simple formula^[16–19]

(1) ${\sigma }_{\text{fus}}~\mathit{P}\cdot \mathit{\pi }{\lambda }^2\text{exp}\left(-B_{\text{G}}/\sqrt{E_{\text{cm}}}\right),$(1)

with the Gamow term^[20,21]

$B_{\text{G}}=31.40Z_{\text{t}}{Z}_{\text{p}}\sqrt{\text{keV}}$

where Z_p and Z_t are the atomic numbers of the projectile and target, and E_cm and ƛ are the kinetic energy and reduced wavelength, all in the center-of-mass frame. P was often assumed to be a constant scaling factor.^[17]

In the 1940s, Teller used P ~ 0.3^[17,18] for dd fusion; 0.15 for each of the d(d,n) and d(d,p) channels. Teller’s use of P = 0.15 was to be expected since this was the value needed to match Coon et al.’s Chicago data obtained in the 1942–1944 timeframe^[22,23] that were commissioned by the Manhattan Project.

In the following section, we analyze some of the experimental observations of Oliphant et al.^[3] and infer P = 0.20 ± 0.02 for the d(d,p) reaction. We were surprised by the closeness of this result to the value of Teller,^[17] given that Oliphant et al.^[3] were focused on establishing the reaction mechanism and not the cross sections and our lack of knowledge of some key aspects of Oliphant et al.’s experimental setup.

III. MODELING THE d(d,p) REACTION RATES REPORTED BY OLIPHANT et al

In the dd-fusion discovery paper,^[3] Oliphant et al. observed the d(d,p)t reaction with targets of ND₄Cl, (ND₄)₂SO₄, and D₃PO₄. This was done to confirm that the reaction products were coming from the presence of the deuterons in the target, and not from reactions involving any of the heavier elements in the targets.

However, Oliphant et al.^[3] only reported the absolute proton production rate as a function of the incident energy of the deuterons for the (ND₄)₂SO₄ target (see Fig. 1). The solid angle subtended by the exit window to the detection system was not given in the 1934 discovery paper. Instead, for apparatus details, the reader is referred to an earlier experiment performed in 1933.^[11] However, Oliphant et al. stated early in the 1934 discovery paper that “[i]n the light of experience of the past year, the installation has been modified in several particulars and entirely reconstructed.” The discussion about these changes appears related only to the accelerator and ion source parts of the experimental setup. However, we cannot be sure that the final beam collimating, target, and target window parts of the 1934 setup were the same as in the 1933 description^[11] (see Fig. 2).

Fig. 1. (circles) Oliphant et al.’s 1934 data^[3] for proton generation per μA of deuterons on a (ND₄)₂SO₄ target. (dashed curve) The curves display the corresponding model calculations using Eq. (1)(1) ${\sigma }_{\text{fus}}~\mathit{P}\cdot \mathit{\pi }{\lambda }^2\text{exp}\left(-B_{\text{G}}/\sqrt{E_{\text{cm}}}\right),$(1) with P = 0.20, and (solid curve) using a modern evaluation for the d(d,p) cross sections by Bosch.^[21] Both of these theoretical calculations are for deuterons stopping in a (ND₄)₂SO₄ target as a function of the deuteron energy incident on the front face of the target.

Fig. 2. Beam, target, and detection geometry at the end of Oliphant and Rutherford’s experiment.^[11] Adapted from Fig. 1 and the discussion on page 262 of Ref. [11].

In the 1933 description,^[11] the solid angle for the detection of the reaction products (particles) was stated to be “… approximately 0.7.” Given the lack of definitive documentation of this part of the 1934 setup, we here have assumed the detection solid angle in the 1934 experiment was also 0.7 sr as depicted in Fig. 2. However, we cannot rule out that the low proton rates from the earlier experiments^[6,7] (see Sec. I) led them to push their detection solid angle up to a value larger than 1.0 sr. The lack of some details needed to enable an unambiguous inference of cross sections is not surprising given that many of the earlier nuclear reaction papers from the Cavendish focus on the discovery of the reaction mechanisms and their associated Q-values, with little to no discussion of the corresponding cross sections.

Given the historical perspective of this paper, we only use computational techniques that were available to the authors in the late 1930s and 1940s. The hand-based calculation methods used here, which have been described in this issue,^[19,24] use ion stopping powers^[25] and fusion cross sections^[21] and have been implemented in a small Excel spreadsheet. The stopping powers for deuterons slowing in (ND₄)₂SO₄ are displayed in Fig. 3.

Fig. 3. Stopping powers for deuterons slowing in (ND₄)₂SO₄.

Our calculated proton detection rates are compared to the observations of Oliphant et al.^[3] in Fig. 1, and were obtained by multiplying the calculated probability that an incident deuteron induces a d(d,p) reaction by 6.24 × 10¹² deuterons per second per μA of beam current, multiplied by the solid angular fraction of the detection system ~0.7/4π ~1/18. We have not allowed for the nonisotropic angular distribution of the d(d,p) reaction because in the 100- to 200-keV region, the peaking in the forward and backward directions are ~60%^[16] larger than the emission near 90 deg (in the center-of-mass frame) and the relevant corrections to our calculation for the Oliphant et al. rates would be to decrease them by ~10% to 20%. For deuteron energies <100 keV, the angular distributions are even weaker with corrections <10%.

Worrying about corrections at this level is not warranted given the other uncertainties associated with not knowing the precise details of the experimental setup. The calculated rates using the cross section from Bosch^[21] are about a factor of 2 lower than the rates reported by Oliphant et al.^[3] and thus Oliphant et al.’s results suggest cross sections about twice the modern values. Despite this discrepancy, the deuterium beam energy dependence of Oliphant et al.’s d(d,p) proton production rate is clearly consistent with the quantum mechanical tunneling through the Coulomb barrier associated with the fusion of two hydrogen isotopes. At each Oliphant et al. deuteron beam energy, we can use the ratio of their proton detection rate to that predicted by our modern calculation (see the solid curve in Fig. 1) to infer d(d,p) cross sections, which we report in Table I, at the corresponding average deuteron energies causing d(d,p) reactions in the (ND₄)₂SO₄ target.

TABLE I d(d,p) Cross Sections Inferred from the Proton Detector Rates Displayed in Fig. 3 of the Oliphant et al.^[3] Discover Paper*

Ed (keV)	${\overline{E}}_{\mathit{d}}$ (keV)	Ratio	d(d,p) (mb)
			Bosch	Inferred
24	20	6.8	0.27	1.8
36	29	2.3	1.1	2.4
51	40	1.7	2.6	4.4
65	49	1.6	4.4	7.0
85	63	1.9	7	14
129	92	2.4	14	33
160	111	2.3	18	41

*Both the energy of the deuteron beam incident on the (ND₄)₂SO₄ target E_d and the mean energy of the deuterons inducing d(d,p) reactions ${\overline{E}}_{\mathit{d}}$ are listed. The cross sections from the modern evaluation of Bosch^[21] are at the mean energies ${\overline{E}}_{\mathit{d}}$. The inferred cross sections were obtained by multiplying the Bosch values by the ratio of Oliphant et al.’s proton detector rates to the corresponding points on the solid curve displayed in Fig. 1.

To perform an analysis similar to what could have been done soon after the results of Oliphant et al.^[3] were published, we assume the d(d,p) cross section to be of the form of Eq. (1)(1) ${\sigma }_{\text{fus}}~\mathit{P}\cdot \mathit{\pi }{\lambda }^2\text{exp}\left(-B_{\text{G}}/\sqrt{E_{\text{cm}}}\right),$(1) and adjust P to obtain a match to the Oliphant et al. data. The corresponding match with P = 0.20 ± 0.02 is displayed by the dashed curve in Fig. 1. This simple model is consistent with Oliphant et al.’s (ND₄)₂SO₄ data at the ~20% level for all but the lowest (23-keV) data point. The uncertainty in our inference for P is due to a combination of the 20% scatter mentioned previously, and an assumed detection solid angle of 0.70 ± 0.05 sr.^[11] Our value of P ~ 0.2, inferred from the Oliphant et al. d(d,p) data, is about 1/3 larger than the value used by Teller.

The reported proton production rates of Oliphant et al.^[3] are a factor of 2 larger than our model calculations when we used a modern assessment^[21] (see Fig. 1), and suggest a simple factor missing from our simulations that is common to all beam energies. In my view, Oliphant et al.’s^[3] description of their beam current measurements rules out a systematic halving of this value. We have searched for other causes of the factor of 2 inconsistency and have found none, except for our lack of knowledge of the 1934 detector solid angle. We again remind the reader that Oliphant et al. did not attempt an inference of the d(d,p) cross sections from their observations, nor did they give the solid angle for their detection of protons in their 1934 paper. Here we have assumed a detection solid angle of ~0.7 sr as referenced in a description of an earlier experimental setup used by Oliphant et al. in 1933.^[11]

The measured Oliphant et al.^[3] d(d,p) reaction rates have a dependence on accelerator voltage (see the dashed curve in Fig. 1) consistent with the Gamow term associated with the quantum mechanical Coulomb barrier penetration associated with the fusion of two Z = 1 nuclei. If a similar analysis had been performed in 1934, this would have added more evidence to the already convincing case provided by Oliphant et al.^[3] that the d(d,p) reaction proceeded through an excited ⁴He nucleus before breaking up into a proton and a triton.

Disclosure Statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the U.S. Department of Energy.