The shell effects in s-wave neutron resonance level densities ρ according to combinatorial calculations and on the basis of the semi-classical approach

Abstract

The results of calculations of level densities ρ, in the vicinity of the neutron binding energy Sn, are presented. These results were obtained using the Böhning combinatorial method for the calculation of particle-hole state densities dependent on the number of decompositions of the nucleus excitation energy to energies of independent fermions. The calculation was based on the semi-classical model description in the computation of particle-hole state densities and then of the level densities ρ, and takes into account the existence of energy gaps Δ, located near the Fermi level, in a single particle level scheme. This procedure considerably improved and extended the Böhning calculation method. The results, which were obtained in this way for ρ, for 220 nuclei, reproduce the regularities observed in the experimental values of ρ, which are dependent on the neutron number N, and they agree with the experimental data within two orders of magnitude. In addition, the neutron resonance densities ρ were calculated on the basis of the particle-hole state densities obtained using the analytical formula from Böhning's paper. To make the calculations possible, the values of ‘complexity’ k, as given in the semi-classical model, and the spin factors R(J), according to the paper by Ryckbosch, were used.