Level Density of a System of Fermi Particles

Formulas for the density of the energy levels of a system of independent Fermi particles are derived which are valid for all values of the excitation energy, and thus a criterion for the validity for the usual (high-degeneracy) formulas is obtained. It is shown that as the energy of the system increases, the degree to which the usual (high-degeneracy) formulas are modified, depends strongly on the distribution of the individual-particle levels. If the levels are spaced uniformly, the corrections are especially small. Applications to nuclei are discussed briefly.