Level Density of a Fermi Gas: Average Growth and Fluctuations

We compute the level density of a two-component Fermi gas as a function of the number of particles, angular momentum, and excitation energy. The result includes smooth low-energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy-Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low-lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.

Figure 1

Entropy $\mathcal{S}$ as a function of the mass number $A$ for nuclear level densities at neutron threshold. (a) experimental values; (b) theoretical prediction; (c) relative error.