Nuclear level densities at high excitation energies and for large particle numbers

Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density ρA(E) and to particle-hole densities. We use exact expressions for the low-order moments and cumulants to derive approximate expressions for the coefficients of an expansion of these densities in terms of orthogonal polynomials. The approach is asymptotically (mass number A≫1) convergent and, for large A, covers about 20 orders of magnitude near the maximum of ρA(E) (i.e., about half the spectrum). Densities of accessible states are calculated using the Fermi-gas model.