Nuclear Constitution and the Interpretation of Fission Phenomena

An attempt is made to correlate in a unified picture the features of the empirical evidence on nuclear constitution, some of which appear to require for their explanation the liquid drop model as others require the independent particle picture. As an idealized and exploratory basis for an inclusive description, the extreme saturation assumption has been adopted: potential on a typical nucleon in the nuclear interior nearly independent of the position of the other nucleons, this potential falling off in a small distance at the nuclear surface. In the resulting collective model of the nucleus a distinction is made between the nucleonic state of the system—as defined by the states occupied by the individual nucleons—and the state of vibration and rotation of the nucleus as a whole. On quantum-mechanical grounds it is shown how the kinetic energy of this motion receives an explanation in terms of the degrees of freedom of the individual particles. As in the electronic-vibrational-rotational description of molecular constitution, so in the case of the nucleus it is reasonable to think of the sums of the energies of the individual particle states, plus the sum of the interaction energies, as defining a potential energy of deformation as a function of the shape of the system. Different states of the totality of individual particles give rise to different potential energy surfaces. A given sheet touches one of the surfaces immediately above or below it only at certain isolated "funnels" as in the case of polyatomic molecules. For full validity of the collective model it is necessary that nonadiabatic transitions from one surface to another occur infrequently compared to the frequency of rotation and capillary oscillations, so that these collective motions have a well-defined existence. The mathematical consequences of the collective model have not been explored fully enough to tell whether this condition of self-consistency is fulfilled well or very roughly or not at all for any given excitation energy. The vibrational freuencies correspond in general terms to those predicted by the simple liquid drop model, with, however, certain characteristic quantum mechanical differences. Instances of the Franck-Condon principle have to be accepted, analogous to those in the molecular case. Discussed are some consequences of the collective model or of its liquid drop simplification for energy levels, compatibility of strong neutron capture with individual particle effects in binding, quadrupole moments, alpha-decay, fission thresholds, photofission, spontaneous fission, asymmetry in nuclear fission, hydrodynamics of the division process, fission alpha-particles, and fragment excitation.