Compatibility of the nuclear shell and nucleon bag models.

Abstract

For the theoretical treatment of a realistic many-body system it is necessary to introduce a model with a manageable number of degrees of freedom as a zero order approximation. In most cases the choice of such a model is suggested by the experimental observation of some qualitative properties of the system. The hope is that the more detailed properties will be given by calculable corrections to the zero order model. Once a model has been formulated, the theory has the minimum task of showing its self-consistency: the essential assumptions of the model should not be clearly invalidated by the corrections. The present paper studies this self-consistency problem for the case of the nuclear independent-particle model with bag-like nucleons. A good part of the successful calculations performed in nuclear physics during the last thirty years has been based on the assumption that the independent-particle model is a good zero order approximation to the nucleus. The essence of this model is the hypothesis that any particular nucleon behaves in the nucleus as a particle of a Fermi sea, moving in a smooth potential and having a mean free path which is large compared to the nuclear dimension. Historically, the experimentally observed validity of the nuclear shell model 1 was quite surprising, beca use the large nucleon-nucleon cross sections had earlier lead to the belief that the nucleons in a nucleus would be similar to the molecules in a liquid drop, having a very small mean free path. In respect to the experimental situation, it should be stressed that the validity of the shell model is a much stronger statement than the existence of low energy single-particle-like excitations, which are not uncommon in Fermi systems. 2 In fact, the single-particle behavior of the nucleons appears to be almost literally true.3 This behavior is, for example, evident in quasifree scattering4 and in the often quite nontrivial quantum numbers of the loosely bound nucleons in heavy nuclei. 5 The compatibility of the large size of the low energy cross sections with the shell model was recognized by Weisskopf.6 He remarked that in the independent-pair model the Pauli exclusion principie drastically reduces the effects of the nucleon-nucleon interaction because the low-lying single-nucleon states are already occupied. This argument was quantitatively confirmed by means of the Bethe-Goldstone equation, 7 which allows us to show that