The mechanism of nuclear fission. Offprint from Physical Review, Vol. 56, No. 5, September 1, 1939 by BOHR, Niels & WHEELER, John Archibald - 1939

American Physical Society: Lancaster, PA, 1939. First edition. THE STANDARD THEORY OF THE MECHANISM OF NUCLEAR FISSION - ESSENTIAL FOR THE DEVELOPMENT OF THE ATOMIC BOMB.

First edition, extremely rare offprint, of this seminal paper, which presents the first comprehensive theory of nuclear fission, discovered just six months earlier by Otto Hahn and Fritz Strassmann. This theory was essential for the development of the atomic bomb. "The theory of Bohr and Wheeler was accepted, and continued to remain ever since, as the standard description of the mechanism of nuclear fission" (Mehra & Rechenberg, The Historical Development of Quantum Theory 6, p. 1006). "Wheeler's technical mastery of physics is best seen in the classic paper of Bohr and Wheeler, 'The Mechanism of Nuclear Fission' (1939), published on the day when Hitler's armies marched into Poland and World War II began. Bohr and Wheeler wrote the paper in Princeton, where Bohr was visiting in the spring of 1939, a few months after the discovery of fission. The paper is a masterpiece of clear thinking and lucid writing. It reveals, at the center of the mystery of fission, a tiny world where everything can be calculated and everything understood. The tiny world is a nucleus of uranium 236, formed when a neutron is freshly captured by a nucleus of uranium 235. The uranium 236 nucleus sits precisely on the border between classical and quantum physics. Seen from the classical point of view, it is a liquid drop composed of a positively charged fluid. The electrostatic force that is trying to split it apart is balanced by the nuclear surface tension that is holding it together. The energy supplied by the captured neutron causes the drop to oscillate in various normal modes that can be calculated classically. Seen from the quantum point of view, the nucleus is a superposition of a variety of quantum states leading to different final outcomes. The final outcome may be a uranium 235 nucleus with a re-emitted neutron, or a uranium 236 nucleus with an emitted gamma-ray, or a pair of fission-fragment nuclei with one or more free neutrons. Bohr and Wheeler calculate the cross-section for fission of uranium 235 by a slow neutron and get the right answer within a factor of two. Their calculation is a marvellous demonstration of the power of classical mechanics and quantum mechanics working together. By studying this process in detail, they show how the complementary views provided by classical and quantum pictures are both essential to the understanding of nature. Without the combined power of classical and quantum concepts, the intricacies of the fission process could never have been understood. Bohr's notion of complementarity is triumphantly vindicated" ('John Archibald Wheeler,' Proceedings of the American Philosophical Society 154, No. 1, March 2010, pp. 126-7). OCLC lists 2 copies (one in US). No copies on RBH.

Provenance: Abraham Pais (1918-2000), Dutch-American Jewish theoretical physicist. After the War, Pais studied with Bohr in Copenhagen, before taking up a position at the Institute for Advanced Study in Princeton, where he worked from 1947 until 1963 on the physics of elementary particles. In later life, Pais became interested in documenting the history of modern physics, feeling that he was in a unique position to do so having known personally many of the main protagonists. This resulted in his acclaimed biographies of Einstein (Subtle is the Lord, 1982) and Bohr (Niels Bohr's Times, 1991), as well as several other published works.

"In the late 1930s, a series of experiments showed that bombarding uranium with neutrons produced several new radioactive elements, which were assumed to have atomic numbers near to that of uranium (Z = 92). This assumption followed naturally from the prevailing view of nuclear decay, which involved the emission, through tunnelling, of only small charged particles (α and β). How then did one explain the formation of an element which was, as far as could be determined, identical to barium (Z = 56), and thus much smaller than uranium?" (Nature Physics Portal)."Experiments conducted in 1938 at Berlin by Hahn and Strassmann were reported to Lise Meitner, an Austrian scientist who had fled to Copenhagen to escape religious persecution. She and her nephew, O. R. Frisch, working in Niels Bohr's laboratory, found the true explanation of these phenomena. The interpolation of a neutron into the nucleus of a uranium atom caused it to divide into two parts and to release energy amounting to about 200,000,000 electron volts. This process bore such a close similarity to the division of a living cell that Frisch suggested the use of the term 'fission' to describe it" (PMM).

Meitner and Frisch explained the fission process by viewing the nucleus like a liquid drop, following a model that had been proposed in 1928 by the Russian physicist George Gamow and then extended by Bohr in 1936 into what became known as the 'compound nucleus model'. The idea was that, after being hit with a neutron, the uranium nucleus might, like a water drop, become elongated, then start to pinch in the middle, and finally split into two drops. After the split, the two drops would be driven apart by their mutual electric repulsion at high energy, about 200 MeV, Frisch and Meitner calculated. Where would the energy come from? Meitner determined that the two daughter nuclei together would be less massive than the original uranium nucleus by about one-fifth the mass of a proton, which, using Einstein's famous formula, E = mc2, works out to 200 MeV, exactly as it should be.

When Frisch returned to Copenhagen with the news, Bohr immediately exclaimed 'Oh, what idiots we have all been! Oh, but this is wonderful!' Bohr was then preparing to depart for the United States via Sweden and England. He had been invited on his previous visit ot the US to spend a term at the Institute for Advanced Study. Bohr confirmed the validity of the findings while sailing to New York City, arriving on January 16, 1939. Ten days later Bohr, accompanied by Enrico Fermi, communicated the latest developments to some European émigré scientists who had preceded him to the United States and to members of the American scientific community at the opening session of a conference in Washington D.C. "The Fifth Washington Conference on Theoretical Physics, sponsored jointly by George Washington University and the Carnegie Institution of Washington, began January 26, 1939, with a discussion by Professor Bohr and Professor Fermi of the remarkable chemical identification by Hahn and Strassmann in Berlin of radioactive barium in uranium which had been bombarded by neutrons. Professors Bohr and Rosenfeld had brought from Copenhagen the interpretation by Frisch and Meitner that the nuclear 'surface tension' fails to hold together the 'droplet' of mass 239, with a resulting division of the nucleus into two roughly equal parts. Frisch and Meitner had also suggested the experimental test of this hypothesis by a search for the expected recoil-particles of energies well above 100,000,000 electron-volts which should result from such a process. The whole matter was quite unexpected news to all present" (Peierls, p. [56]).

"The genesis of the [present paper] is described by Wheeler in a talk, from which the following extracts are taken [Some Men and Moments in the History of Nuclear Physics, pp. 217-306 in: Nuclear Physics in Retrospect. Proceedings of a Symposium on the 1930s (ed. R.H. Stuewer), 1979]:

'Once Bohr arrived in Princeton, we set to work to go from Frisch and Meitner's broad-brush picture to a detailed analysis of the mechanism along the lines of the compound nucleus model and liquid drop model that Bohr - and I - had already been expounding and applying. This work took not only the three months of Bohr's stay in Princeton but two additional months of finishing up until I could send it in for publication (June 28, 1939)

'The whole enterprise was very much to Bohr's taste, liking as he did to see any part of physics with which he was concerned brought together in a comprehensive and harmonious whole. In addition, he had always loved the subject of capillarity. For one of his first pieces of student research he had experimented on the instability of a jet of water against breakup into smaller drops ...

'A new feature of capillarity entered in the case of fission, the concept of fission barrier. The very idea was new and strange. More than one distinguished colleague objected that no such quantity could even make sense, let alone be defined. According to the liquid drop picture, is not an ideal fluid infinitely subdivisible? And therefore cannot the activation energy required to go from the original configuration to a pair of fragments be made as small as one pleases? We obtained guidance on this question from the theory of the calculus of variations in the large, maxima and minima, and critical points. This subject I had absorbed over the years by osmosis from the Princeton environment, so thoroughly charged by the ideas and results of Marston Morse. It became clear that we could find a configuration space to describe the deformation of the nucleus. In this deformation space we could find a variety of paths leading from the normal, nearly spherical configuration over a barrier to a separated configuration. On each path the energy of deformation reaches a highest value. This peak value differs from one path to another. Among all these maxima the minimum measures the height of the saddle point or fission threshold or the activation energy for fission. The fission barrier was a well-defined quantity!

'Bohr knew from earlier days that a work of Lord Rayleigh would have something to say about the capillary oscillations of a liquid drop. We rushed up to the library on the next floor of Fine Hall and looked it up in the Scientific Papers of Rayleigh. This work furnished a starting point for our analysis. However, we had to go to terms of higher order than Rayleigh's favorite second-order calculations to pass beyond the purely parabolic part of the nuclear potential, that is, the part of the potential that increases quadratically with deformation. We determined the third-order terms to see the turning down of the potential. They enabled us to evaluate the height of the barrier, or at least the height of the barrier for a nucleus whose charge was sufficiently close to the critical limit for immediate breakup.'

"A full calculation of the height of the barrier would have been too difficult, and much ingenious work on this has been done by several authors since then. Wheeler continues:

'For our immediate needs, however, our simple 'poor man's' interpolation was adequate. With it, knowing - or estimating from observation - the fission barrier for one nucleus, we could estimate the fission barrier for all the other heavy nuclei, among them plutonium 239. Thanks to the questioning of Louis A. Turner ... we came to recognize that this substance, which up to then one had never seen except through its radioactivity ... would be fissile ...

'The barrier height of a compound nucleus against fission was not the only factor relevant for fission. Equally important in governing the probability of this process was the excitation, or 'heat of condensation', delivered up by the uptake of a neutron to form the compound nucleus in the first place

'Fortunately Bohr and I had just been through the systematics of nuclear energies in the course of calculating the release of energy in various actual and potential fission processes. Therefore, we could estimate the difference between the excitation developed by neutron capture in the two uranium isotopes as almost a million volts, in favor of fission of U235. From our interpolation for fission barriers we estimated on the other hand a barrier almost 1 MeV lower for U235 than for U238 ...

'Placzek, wonderful person that he was, a man of the highest integrity, often a thoroughgoing skeptic about new ideas, said to me over and over in those early spring days of 1939 that he could not believe that the small amount of U235 could be the cause of the slow neutron effects in natural uranium. I therefore bet him a proton to an electron, $18.36 to a penny, that Bohr's diagnosis was correct. A year later Alfred Nier at Minnesota had separated enough U238 to make possible a test and sent it to John Dunning at Columbia to measure its fission cross section. On April 16, 1940, I received a Western Union money order telegram for one cent with the one-word message 'Congratulations!' signed Placzek.'

"Bohr's judgment had been proved right.

"In July 1939, Wheeler sent Bohr the proofs of the paper. Bohr's reply is along not unfamiliar lines:

'I read through it with great pleasure and admiration for all the work you have done with it and it was of course very tempting to wire that it could be published in the present state. Still I felt that a few smaller alterations were advisable and I hope that the delay of publication caused by this letter will only be small.'

"The paper was published on 1 September 1939. It remains today the basis of our description of the fission process.

"Bohr immediately realised the relevance of the theoretical results for the question of the possibility of a chain reaction. In an unpublished note dated 5 August 1939 he discusses the conditions for this and concludes that no chain reaction is possible in ordinary uranium without the presence of a moderator, i.e., a substance containing light nuclei which would slow down the neutrons to thermal velocities, but that the situation would be very different for isotopically pure or substantially enriched uranium" (Peierls, pp. [69]-[72]).

Peierls, Introduction to: Niels Bohr CollectedWorks, Vol. 9 (Peierls, ed.), 1986.

Large 8vo (267 x 199 mm), pp. 426-450, [3, blank] (small crease to upper outer corner) Original printed wrappers (a bit darkened at the edges).