The higher random phase approximation and the stability of the energy spectrum of the nuclear shell model

Abstract

Assuming only two-body nuclear forces, we study the dynamical two and many-nucleon correlations in spherical nuclei with the method of the Heisenberg equations of motion of the one-nucleon operators. After self-consistently solving the Hartree-Fock problem for the shell model we study the effect of the left-over non linear coupling terms using the method of the Higher Random Phase Approximation (HRPA). In particular, we formulate the secular problem and solve it in the Second Random Phase Approximation (SRPA) for spherical nuclei. The numerical work has been carried out for the example of the16O nucleus. The original Hartree-Fock shell model spectrum has been found rather stable against the inclusion of the « triple » correlations. The density fluctuation terms have been shown to be rather small, but, generally, capable of introducing a certain damping of some of the single-particle states as a consequence of the non-hermiticity of the extended SRPA secular matrix.