# Fermi gas descriptions of nuclear level densities

Article

In this paper the derivation of nuclear level densities from a Fermi gas treatment of the nucleons is surveyed. In fact, there are three classes of Fermi gas models: the infinite, in which an unlimited number of fermions are available for excitation, the finite, in which this number is finite but the single-particle spectrum is unbounded, and the truncated Fermi gas (TFG), where this spectrum consists of a finite number of levels. Exact calculations within the TFG are possible by means of combinatorial methods, while the finite model may be analysed by assuming that the assumptions of statistical mechanics apply to the numbers of nucleons in a nucleus and then using a saddle point approximation. The standard Bethe formulae actually correspond to the infinite model and apply to the other models only in the low-energy limit. Furthermore, at very low energies they do not approximate any of the models with high accuracy and should there be corrected, as indicated in the text. For high-energy or high-temperature applications, it is essential to take into account the effects of truncation. The TFG is constructed here in a way which accommodates the two main features in which the results for real interacting nucleons should differ from the Fermi gas picture. In order to make the TFG results accessible for practical applications without having to perform the cumbersome combinatorial calculations for each case of interest, simple approximations are presented for the nuclear level densities, as well as the closely related canonical partition functions, as obtained by means of calculations using the truncated Fermi gas model. © 1991.