A new method to calculate level densities for non-interacting Fermions within the constant-spacing model with a finite number of states is developed. We show that asymptotically (for large numbers of particles or holes) the densities have Gaussian form. We improve on the Gaussian distribution by using analytical expressions for moments higher than the second. Comparison with numerical results shows that the resulting sixth-moment approximation is excellent except near the boundaries of the spectra and works globally for all particle/hole numbers and all excitation energies.

14 pages, 4 figures; v2 updated to the published version - extended the motivation; results unchanged