Generalized Bethe formula for the total level density

It is pointed out that the generalized Bethe formula for the total level density encompasses the standard Bethe formula and the constant temperature formula as limiting cases. It is shown that the generalized Bethe formula provides an excellent fit to the results of combinatorial calculations in the region of doubly closed shell nucleus ${}^{208}\mathrm{Pb}$ where the standard Bethe formula fails. The new parameter $\xi$ associated with the generalized Bethe formula shows a systematic behavior with distance from double shell closure.