Analytic Nuclear Level Density Formula with Shell and Pairing Effects

Abstract

For use in calculations and in analyses of experimental data an analytic approximation of the level density is worked out. This is done in two steps. First the level density is calculated in a simple but realistic model including both shell structure and pairing effects. Then it is approximated by an analytic function of the excitation energy together with a few parameters describing average properties of the single particle spectrum. The overall accuracy in the natural logarithm is, for realistic parameters, better than one unit, and for energies above around 5 MeV it is usually better than 0.5. A detailed prescription to obtain the necessary parameters is given in terms of experimental binding energies and the observed level density at the neutron binding energy. The resulting energy dependent level density is compared with observations available for energies below 8 MeV for several nuclei. Systematic deviations are found for the lighter nuclei. Very good agreement is obtained for heavier nuclei.