  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.
