Macroscopic systematics of nuclear level densities

Abstract

In a number of recently proposed semi-empirical nuclear level density formulae, a macroscopic-microscopic approach similar to that used in nuclear potential energy calculations has been successfully used. While the underlying macroscopic part in these formulae is the well-known Bethe expression, these fomulae differ in the treatment of the microscopic part, namely the shell and pairing effect. In the present work, we have carried out a study of the macroscopic features of the nuclear level densities on the basis of the independent-particle model of the nucleus. It was found that even after taking into account shell and pairing effects, large deviations from the predictions of the Bethe expression with a level denisty parameter a smoothly dependent on the mass number ( a = αA) are present. In particular, the level density parameter a was found to be strongly dependent on the last nucleon separation energies. A simple parametrisation of a including its dependence on the separation energies is proposed. The experimental data on the neutron resonance spacings of spherical nuclei have been analysed on the basis of this parametrisation. It is shown that the predicted isospin dependence of a is consistent with the available experimental data. The deformation dependence of a is also discussed.