A CRITICAL REVIEW ON SOME ASPECTS OF concepts we use up to the present day can be found in their work THE THEORY OF FISSION (Ref. 50). The general picture of this process is as follows: When a H.C. PAULI nucleon, say a neutron, impinges on a heavy nucleus like uranium, it is absorbed. The nucleus gains some energy as a result of Max-Planck-Institutefur Kemphysik, this reaction, and goes through a series of complicated intermed- Heidelberg, iate states about which we have little information. One refers to Federal Republic of Germany this entity of states as the compound nucleus (Ref. 51, 248), an idealized concept introduced by N. Bohr (Ref. 52). After some time long as compared to all other characteristic times, say after — 1 8 Lecture notes by Drs. V.S. Ramamurthy and S.K. Kataria 10 seconds, the nucleus eventually fissions. The deexcitation by fission is accompanied by or is in competition with other reac- Abstract. The lecture notes display briefly some of the facets tions such as the emission of beta or gamma radiation or the emis- which eventually will be part of a theory for the fission process. sion of particles, mostly neutrons. They cover some important aspects of our present understanding in The emission of two to three neutrons on ths average per fis- a qualitative fashion and complement the existing review articles sion event is particularly important. They maintain the chain rather than replacing them. The notes include sections on (I) The reaction, and allow for the burning of the nuclear fuel. The Bohr-Wheeler Fission of a Drop, (II) The Strutinsky-Swiatecki economic, sociological, and environmental implications of this Quantum Droplet, (III) The Question of Inertias of a Fluid in Mo- reaction are known, and cause the practical interest in this pro- tion, (IV) Some Selected Aspects of the Distributions of Mass and cess. On the other hand, Kinetic Energy, and (V) Possible Relations Between the Phenomeno- "The fission process has occupied a unique place in the de- lo lical Models and Self-Consistent Field Approximations. velopment of nuclear physics, but should be recognised as part of a wider range of phenomena involving large-scale nuclear deformations and collective flow that are now becoming acces- sible in the study of reactions produced by accelerated heavy ions." (Ref. 47). I. Introduction Fission is the process in which a heavy nucleus splits into two It might seem surprising that even four decades after the dis- fragments of nearly equal masses, either spontaneously or as a covery of the process a complete and consistent description of result of a reaction. It was discovered by Hahn and Strassmann the fission process does not exist. Almost uniquely in nuclear (Ref. 144) in 1939, and in analogy to the division of a biologi- physics, one is faced with the full complexity of the many-body cal cell the term "fission" was coined by Meitner and Frlsch problem, which in turn makes fission an ideal testing ground for (Ref. 254) soon after. These authors also gave the first quali- the various methods and descriptions. The models developed in the tative interpretation of Hahn and Strassmann's observations, and past to stress the various aspects such as collective and single in particular mentioned the possibility of a large energy release particle motion, fluid dynamics, and single particle motion often in this type of reaction. The foundations for understanding the contradict each other. All of them find some support in different mechanisms were laid by N. Bohr and J.A. Wheeler, and many of the classes of experiments, but for the further progress it seems a J« necessity and a challenge to disentangle their mutual relations Wheeler's fundamental concepts (Section II) seemed a necessary and possible overlap. prerogative for the description of subsequent developments. The Any presentation of the theory of fission - the present one modification of the potential energy is treated in Section III. included - must suffer from these facts, and cannot give more The questions related to the collective inertia (Section IV) are than an unsatisfactory enumeration of the models. Also the lit- tightly interwoven with the problematics of nuclear collective terature reflects the situation. Only two monographs deal with motion. Attempts to understand some aspects of the multidiffer- nuclear fission (Ref. 1, 2). The books of Hyde (Ref. 169) deal ential fission cross sections are presented in Section V. For an with many aspects of fission. The booklet of Wilets - despite eventual reaction theory of the fission process, one seemingly being outdated slightly by some of the newer developments - is needs ideas which go beyond the usual concepts. The phenomenolog- still worth reading, because of its succinct account of the es- ical aspects are collected in Sections II to V. One can relate sential ideas. A rather complete account of the various develop- some of them to the less phenomenological self-consistent field ments can be found in the proceedings of the IAEA symposia on the methods. The need for an almost stenographic shortness of these physics and chemistry of fission (Ref. 3, 5, 8). The proceedings notes becomes particularly obvious in the last section. Most of of the Nobel symposium on superheavy nuclei (Ref. 6) contain many the formal apparatus had to be omitted and the comparison with ex- numerical results. The bulk of information can also be found in periment is less extensive than would correspond to good tradition more recent review articles (P.ef. 55, 59, 85, 302, 319). and the taste of the author. The aim of the lectures is to complement the existing litera- ture by presenting the essential concepts with a minimum of for- mal definitions and to accompany them with critical comments. II. The Bohr-Wheeler Fission of a Drop This should facilitate the orientation of the scholar and pave The concepts which allow for a qualitative understanding of the the way for future improvement, but it cannot replace a careful fission process have been developed by Bohr and Wheeler (Ref. 50). study of the relevant literature. Even today, they are basic ingredients of our understanding, and, In supporting this study, special care was taken in the List therefore, their salient features will be. briefly displayed. of References. Quite unusually it contains the title of the con- tribution, which should facilitate the orientation. Despite 432 1. Saturation and the Nuclear Binding Energy citations, the list is not complete. Virtually all references to The volume occupied by the nuoleons in a nucleus is roughly pro- experimental work are omitted; some of these can be found in portional to their number. This empirical fact is called satura- Weigmann's lecture (Ref. 418). Only published work was included. tion: The density in the central region is roughly independent Contributions to Letter Journals, which were followed by exten- of the nucleon number A. Since the volume is finite, the density sive articles on the same subject, have been omitted. Questions must drop to zero relatively fast in a surface region. Empirically, of priority therefore cannot be decided by this list! Although I the thickness of the surface layer does not depend on A either. strived for completeness in the aspects of fission, I have to Figure 1 shows a typical nuclear density in a commonly accepted apologize for having missed possible important contributions. parameterization. The present lecture notes are arranged in five sections, which Saturation leads to a characteristic behavior of the binding contain less material in more condensed form than did the oral energy of a nucleus B (understood as the absolute difference be- 42 presentation. The rather extensive reproduction of Bohr and tween the physical mass and the sum of masses of the constituents). The (nuclear part of the) binding energy per particle must tend order on proton (Z) and neutron (N) number, i.e., ai = cl<1 + KiI ) to a constant in the limit of large particle number. Corrections with I = (N - Z)/(N + Z) (Ref. 40, 291). for finite systems can come only for particles in the surface lay- 2. The Static Stability Against Fission er. Their number relative to the total is proportional to A , and since this is a small quantity, it can be used as ordering pa- The binding energy per particle shows a pronounced maximum for rameter in a series (Ref. 287). mass numbers A around A - 60 (see Figure 2). For lighter masses a division of the nucleus would be endothermic, but heavier nuclei In practice, one restricts oneself mostly to the first two are potentially unstable against division. What prevents the fis- terms, called the volume and surface energy, E,, = sion of these nuclides? = ,2/3 respectively. Adding the electrostatic Coulomb energy 2 1/3 It is remarkable that this question was raised only after fis- Ec(o) = C3Z /A one writes for the series sion was detected. Bohr and Wheeler answer this question by "B = Ec(o) means of a deformation energy and argue in the following way: The transition from one dropletlike structure of the fissioning nu- and determines the coefficients (a , a , and c^) by a fit to the v g cleus to the two of the fission fragments does not occur abruptly, nuclear masses. Saturation leads thus to a kind of WeizsScker's but the density proceeds continuously through a sequence of shapes. semiempirical mass formula (Ref. 420) . One particular mass fit This is possible by a deformation of the surface layer, while the is shown in Figure 2. It may serve as an example for the general central density remains essentially unchanged because of satura- properties: tion.