SEPTEM BER 1, 1939 P H YSI CAL RE VI EW VOLUME 56 The Mechanism of Nuclear Fission NIELs BoHR University of Copenhagen, Copenhagen, Denmark, and The Institute for Advanced Study, Princeton, ¹mJersey AND JQHN ARcHIBALD WHEELER Princeton University, Princeton, ¹mJersey (Received June 28, 1939) On the basis of the liquid drop model of atomic nuclei, an account is given of the mechanism of nuclear fission. In particular, conclusions are drawn regarding the variation from nucleus to nucleus of the critical energy required for fission, and regarding the dependence of fission cross section fo'r a given nucleus on energy of the exciting agency. A detailed discussion of the observations is presented on the basis of the theoretical considerations. Theory and experiment fit together in a reasonable way to give a satisfactory picture of nuclear fission. IxTRoDUcnoN Just the enormous energy release in the fission HE discovery by Ferry, i and his collaborators process has, as is well known, made it possible to the that neutrons can be captured by heavy observe these processes directly, partly by nuclei to form new radioactive isotopes led great ionizing power of the nuclear fragments, especially in the case of uranium to the inter- first observed by Frisch' and shortly afterwards esting finding of nuclei of higher mass and charge independently by a number of others, partly by number than hitherto known. The pursuit of the penetrating power of these fragments which these investigations, particularly through the allows in the most efficient way the separation from the uranium of the new nuclei formed the work of Meitner, Hahn, and Strassmann as well ' by as Curie and Savitch, brought to light a number fission. These products are above all character- of unsuspected and startling results and finally ized by their specific beta-ray activities which led Hahn and Strassmann' to the discovery that allow their chemical and spectrographic identifi- from uranium elements of much smaller atomic cation. In addition, however, it has been found weight and charge are also formed. that the fission process is accompanied by an emission which seem be The new type of nuclear reaction thus dis- of neutrons, some of to associ- covered was given the name "fission" by Meitner directly associated with the fission, others and Frisch, ' who on the basis of the liquid drop ated with the subsequent beta-ray transforma- model of nudei emphasized the analogy of the tions of the nuclear fragments. process concerned with the division of a Huid In accordance with the general picture of sphere into two smaller droplets as the result of a nuclear reactions developed in the course of the nuclear deformation caused by an external disturbance. last few years, we must assume that any In this connection they also drew attention to the transformation initiated by collisions or irradi- fact that just for the heaviest nuclei the mutual ation takes place in two steps, of which the first is repulsion of the electrical charges will to a large the formation of a highly excited compound extent annul the effect of the short range nuclear nucleus with a comparatively long lifetime, while forces, analogous to that of surface tension, in 3 O. R. Frisch, Nature 143, 276 (1939);G. K. Green and opposing a change of shape of the nucleus. To Luis W. Alvarez, Phys. Rev. 55, 417 (1939);R. D. Fowler and R. W. Dodson, Phys. Rev. 55, 418 (1939); R. B. produce a critical deformation will therefore Roberts, R. C. Meyer and L. R. Hafstad, Phys. Rev. 55, require only a comparatively small energy, and 417 (1939};W. Jentschke and F. Prankl, Naturwiss. N', 134 (1939);H. L. Anderson, E. T. Booth, J. R. Dunning, by the subsequent division of the nucleus a very E. Fermi, G. N. Glasoe and F. G. Slack, Phys. Rev. 55, large amount of energy will be set free. 511 (1939). 4 F. Joliot, Comptes rendus 208, 341 (1939);L. Meitner ' O. Hahn and F. Strassmann, Naturwiss. 2'I, 11 (1939}; and O. R. Frisch, Nature 143, 471 (1939);H. L. Anderson. , see, also, P. Abelson, Phys. Rev. 55, 418 (1939). E. T. Booth, J. R. Dunning, E. Fermi, G. N. Glasoe and ' L. Meitner and O. R. Frisch, Nature 143, 239 (1939). F. G. Slack, Phys. Rev. 55, 511 (1939). 26 M ECHAN IS M OF' NU CLEAR F ISSI ON the second consists in the disintegration of this siderations lead to an approximate expression for compound nucleus or its transition to a less the fission reaction rate which depends only on excited state by the emission of radiation. For a the critical energy of deformation and the prop- heavy nucleus the disintegrative processes of the erties of nuclear energy level distributions. The compound system which compete with the general theory presented appears to fit together emission of radiation are the escape of a neutron well with the observations and to give a satis- and, according to the new discovery, the fission factory description of the fission phenomenon. of the nucleus. While the first process demands For a first orientation as well as for the later the concentration on one particle at the nuclear considerations, we estimate quantitatively in surface of a large part of the excitation energy of Section I by means of the available evidence the the compound system which was initially dis- energy which can be released by the division of a tributed much as is thermal energy in a body of heavy nucleus in various ways, and in particular many degrees of freedom, the second process examine not only the energy released in the requires the transformation of a part of this fission process itself, but also the energy required energy into potential energy of a deformation of forsubsequent neutron escape from the fragments the nucleus sufficient to lead to division. ' and the energy available for beta-ray emission Such a competition between the fission process from these fragments. and the neutron escape and capture processes In Section II the problem of the nuclear seems in fact to be exhibited in a striking manner deformation is studied more closely from the by the way in which the cross section for fission point of view of the comparison between the of thorium and uranium varies with the energy nucleus and a liquid droplet in order to make an of the impinging neutrons. The remarkable estimate of the energy required for different difference observed by Meitner, Hahn, and nuclei to realize the critical deformation neces- Strassmann between the effects in these two sary for fission. elements seems also readily explained on such In Section III the statistical mechanics of the lines by the presence in uranium of several stable fission process is considered in more detail, and an isotopes, a considerable part of the fission approximate estimate made of the fission proba- phenomena being reasonably attributable to the bility. This is compared with the probability of rare isotope U"' which, for a given neutron radiation and of neutron escape. A discussion is energy, will lead to a compound nucleus of then given on the basis of the theory for the higher excitation energy and smaller stability variation with energy of the fission cross section. than that formed from the abundant uranium In Section IV the preceding considerations are isotope. ' applied to an analysis of the observations of the In the present article there is developed a more cross sections for the fission of uranium and detailed treatment of the mechanism of the thorium by neutrons of various velocities. In fission process and accompanying effects, based particular it is shown how the comparison with on the comparison between the nucleus and a the theory developed in Section III leads to liquid drop. The critical deformation energy is values for the critical energies of fission for brought into connection with the potential thorium and the various isotopes of uranium energy of the drop in a state of unstable equilib- which are in good accord with the considerations rium, and is estimated in its dependence on of Section II ~ nuclear charge and mass. Exactly how the In Section V the problem of the statistical excitation energy originally given to the nucleus distribution in size of the nuclear fragments is gradually exchanged among the various degrees arising from fission is considered, and also the of freedom and leads eventually to a critical questions of the excitation of these fragments and deformation proves to be a question which needs the origin of the secondary neutrons. not be discussed in order to determine the fission Finally, we consider in Section VI the fission probability. In fact, simple statistical con- effects to be expected for other elements than thorium and uranium at sufficiently high neutron ' N. Bohr, Nature 143, 330 (1939). ' N. Bohr, Phys. Rev. 55, 418 (1939). velocities as well as the effect to be anticipated in N. BOB IC AND J. A. WH EELER thorium and uranium under deutero~ and proton M(Z, A) = Cg+-', B~'(Z —-', A)' impact and radiative excitation. +(Z ',A—)(-M„iV„—)+3Z'e'/SroA&. (3) Here the second term gives the comparative I. ENERGY RELEASED BY NUCLEAR DIVISION masses of the various isobars neglecting the The total energy released by the division of a inHuence of the difference M„—3II„of the proton nucleus into smaller parts is given by and neutron mass included in the third term and of the pure electrostatic energy given by the hZ = (3fp —ZM;)c', fourth term. In the latter term the usual assump- where Mo and M; are the masses of the original tion is made that the effective radius of the and product nuclei at rest and unexcited.