Exact calculation of level densities for many non-interacting fermions in large model spaces

Abstract

A simple recursive method to calculate exactly level densities with fixed spinJ and parity is presented for an independent particle model of nuclei. This method can be used to calculate fixed particle-hole level densities as well. The results of these exact calculations are compared to those of commonly used approximation methods, like the saddle-point approximation and Gram-Charlier expansion. The former appears to be quite accurate, while the accuracy of Gram-Charlier expansion is strongly dependent on decomposition of then-fermion space into smaller subspaces. Comparison of exactly calculated with experimental densities at the neutron evaporation threshold shows unambiguously that some residual interaction must be introduced to describe nuclei at these excitation energies.