Structure and Properties of Nuclei (1932 -1935) An Annotation by C. F. von Weizsacker, Starnberg Heisenberg's work on nuclear physics was only an episode for him, but an im­ portant one. The work consists mainly of the three publications of 1932 and 1933, stimulated by the discovery of the neutron, with some echoes later in the 1930s. In order to understand the kind of interest Heisenberg took in nuclear physics it may be useful to recall how the concept of nuclear physics came about historically. The concept of the atom sprang from the branch of Greek philosophy con­ nected with the names of Leucippus and Democritus. Atoms were supposed to be the ultimate constituents of everything real; they should have no parts, hence be indivisble. This doctrine was not adopted in the philosophy of the next two mil­ lenia, from Plato to Hegel. The philosophers recognized the inner contradictions of the concept of extended atoms. Kant realized that the regions of space filled by an extended atom are obviously filled also by the parts of the atom; then it might be just an empirical question, whether we can divide these parts. Happily naive towards this problem, the chemists around 1800 introduced ex­ tended atoms of different types as the fundamental constituents of different chemical elements. By 1900 the empirical success of this model had become in­ disputable. It served in physics to establish the statistical foundation of thermo­ dynamics. Ludwig Boltzmann argued against the continuum theory of matter, as advocated again by Ernst Mach and Wilhelm Ostwald, that a thermodynamical equilibrium among the infinitely many degrees of freedom of a dynamical continuum system was impossible. However, Boltzmann's beginning of a precise physical atomic theory also cast a shadow on the concept of the atom itself: one had to exclude the applicability of mechanics to the interior of the atom. The problem of the specific heats of monoatomic gases represented this conflict of the atomic hypothesis with (what is today called "classical") mechanics in an inevitably empirical form. Finally, in 1900 Max Planck solved the paradox of the continuum thermodynamics - in the special case of the radiation field, which was the only continuum for which a precise theoretical description was available - by applying the quantum hypothesis, a hypothesis totally inconsistent with classical mechanics, to the representative of atoms: the harmonic oscillator. At about the same time William Ramsay and Ernest Rutherford proved ex­ perimentally the transmutation of chemical elements into each other in the case of radioactivity. Hence the "atoms" of the chemists had to be divisible. Ruther­ ford distinguished for the first time clearly the nucleus and the outer shells of the atom, on the basis of the scattering experiment of Hans Geiger and Ernest Marsden. Niels Bohr recognized the fact that this empirically substantiated atomic model was mechanically and electrodynamically impossible. He sucess- 183 fully decided against applying the fundamental laws of classical physics to the atom, turning instead to Planck's quantum hypothesis. Thus one learned to decypher the codes of optical spectra and of chemical experiences, notably those contained in the periodic system of elements. Within 15 years there evolved a complete theory of the atomic shells. However, it required as its proper basis a completely new fundamental theory of physics, that is, quantum mechanics, to which Heisenberg made the most important single step in 1925. The physics of the nucleus was shown to be a separate field of research only by this establishment of the physics of atomic shells. The empirical knowledge in nuclear physics proceeded continuously during the two decades between 1910 and 1930, notably by the work of Rutherford's school in England, Curie's school in France, and Otto Hahn and Lise Meitner in Germany. One studied in some detail the radioactive families and the properties of a-, P- andy-rays; Rutherford succeeded in obtaining the first artificial nuclear transmutation; the optical spectra of elements (hyperfine structure) provided information about the nuclear spin; Francis Aston succeeded in measuring the mass defects, i.e., the binding energies of nuclei. The theory of the inner constitution of nuclei, however, remained in the dark. Even quantum mechanics did not immediately solve this riddle, but just demon­ strated that it was unavoidable. A nucleus is characterized by two integer num­ bers, the nuclear charge Z and the atomic mass number A. Light nuclei have A close to the value 2 Z, while for heavier ones A increasingly becomes larger than 2 Z. Hence it seemed obvious to assume the nucleus to be composed of two elemen­ tary particles, for which only the known particles proton and electron seemed to be candidates. Then A had to be identified with the number of protons and A- Z with the number of electrons, hence the nucleus characterized by the integers A and Z contained 2 A- Z elementary particles. When one applied quantum mechanics to this model, however, insoluble difficulties arose. A part of the difficulties were theoretical and concerned questions of principle. The nuclear radius is one hundredth of the Compton wavelength of the electron. If electrons are bound in the nucleus, then their kinetic energy, accord­ ing to the uncertainty relation, should be about one hundred times their rest energy. One did not know any forces which could confine the electron in such narrow dimensions. In any case this appeared to be a problem of an extremely relativistic quantum mechanical nature. People doubted around 1932 whether quantum mechanics and relativity might be united without a completely new theoretical idea. Dirac's wave equation of the electron (1928) led to Klein's paradox: it should be possible to pass a potential barrier larger than 2mc2 (m mass of the electron, c velocity of light in vacuo) by a tunnel effect connected with the transition of positive to negative energy. Hence one did not know how to keep electrons in the nucleus at all. Although Dirac's 'hole' theory solved this problem, it also brought along with it new unexplained infinities; the majority of theoreticians including Heisenberg did not accept it in the beginning, and not before 1933, i.e., after pair production was definitely observed, did their attitude change. In addition two empirical difficulties showed up. One concerned spin and statistics of nuclei with integer A but odd Z. The nucleus N 14 with A = 14 and 184 Z = 7 provided an empirical example. Due to the accepted model it contained 21 particles, hence had to possess half-integer spin and Fermi statistics. However, in reality its spin was integer and it followed Bose statistics. Electrons in the nuclei seemed to lose their spin and their specific statistics. The other difficulty emerged form the continuous energy spectrum of the primary P-rays emitted in P-decay. A good example was provided by RaE; if, as one had to assume, the energies of the initial and of the final nucleus took on sharp values, energy conservation seemed to be violated. Calorimetric measurements revealed that the missing energy was not contained in another kind of radiation which could be absorbed by the sur­ roundings. The reaction to these difficulties by Bohr and Heisenberg has been described by Joan Bromberg in a detailed study on the basis of the scientific corre­ spondence from the years 1930 to 1932 [1]. The results of the study agree com­ pletely with my memories about exactly these years, which I mainly spent in Leipzig with Heisenberg; in many details they go beyond what I could notice then myself. Let me describe here Heisenberg's comprehension of problems, follow­ ing from his discussions with me at that time and interpreted in the light of the later development. Heisenberg already possessed at that time the contours of his conception of the historical development of theoretical physics, which he formulated more than 15 years later in his Dialectica article [2]. He was convinced that this development con­ sists of a sequence of "closed theories", each of which reduces the validity of its predecessor as an approximation to certain fields of application and later on receives the same fate, as it will be confined similarly by its successors. Heisenberg had succeeded himself in establishing such a closed theory, quantum mechanics. He was far from considering it as the final theory of physics, but rather waited with anxious curiosity and unbroken ambition for the next (closed) theory. In this context he viewed at that time the big unsolved questions of cosmology and espe­ cially of biology to be lying in the far future, but he expected soon a further step forward within atomic physics itself. For the possible place where such a step could be made there existed around 1930 two hints. Locally, quantum mechanics ob­ viously constituted the right theory of atomic shells; on the other hand, it was obvious that, if one took seriously the above mentioned problems, quantum mechanics did not provide the right theoretical description of the nucleus. Also one had not succeeded so far to combine in a systematic way quantum mechanics with special relativity theory; the difficulties which sprang up here from the grounds reminded Heisenberg and his close friend Wolfgang Pauli of the difficulties of the Bohr model of atomic constitution in 1924. The problem of the existence of elec­ trons in the atomic nucleus seemed to unite aspects of both quantum theory and relativity theory, and thus focussed the interest notably of Bohr and Heisenberg on nuclear physics. This interest therefore was not a specific interest in the atomic nucleus but rather in the next fundamental theory of physics. How radical the cherished expectations were, one derives most appropriately from the fact that Bohr took the continuous fJ-spectra as a reason to renew his older doubts of 1924 with respect to a more than statistical validity of energy conservation [3].