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 image 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 image) convergent and, for large A, covers about 20 orders of magnitude near the maximum of image (i.e., about half the spectrum). Densities of accessible states are calculated using the Fermi-gas model.