2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189859We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.4 pages, 1 figureNuclear TheoryMesoscale and Nanoscale Physicstext