Generalized Bethe formula (GBF) and combinatorial calculations for the systematics of Pb nuclei

Total level densities and state densities up to 40 MeV of excitation energy are calculated combinatorially for the systematics of Pb nuclei using independent nucleons in the realistic single particle spectra. These combinatorial level densities are well fitted by GBF, both for doubly closed shell nucleus 208Pb and away from the shell closure. The corresponding GBF parameters exhibit smooth behavior with the change of the neutron number N, having pronounced extrema at the double shell closure. The GBF fit to the combinatorial results is compared with the fit of standard Bethe formula (BF) and of the Ignatyuk formula.