Microscopic description of average level spacing in even-even nuclei

A microscopic theoretical approach to the average level spacing at the neutron binding energy in even-even nuclei is proposed. The approach is derived based on the Bardeen-Cooper-Schrieffer (BCS) theory at finite temperature and projection M of the total angular momentum J, which is often used to describe the superfluid properties of hot rotating nuclei. The exact relation of the J-dependent total level density to the M-dependent state densities, based on which the average level spacing is calculated, was employed. The numerical calculations carried out for several even-even nuclei have shown that in order to reproduce the experimental average level spacing, the M-dependent pairing gaps as well as the exact relation of the J-dependent total level density formula should be simultaneously used.