Level density of a Fermi gas: average growth and fluctuations

Patricio Leboeuf ¹, Jérôme Roccia ¹

Physical Review Letters 97 (2006) 010401

We 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.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud