Hartree-Fock-Bogoliubov theory versus local-density approximation
for superfluid trapped fermionic atoms

Marcella Grasso

Department of Physics of University of Catania and INFN, 64 via S. Sofia, 95123 Catania, Italy

I will investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. I will propose a regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov (HFB) equations caused by the use of a zero-range atom-atom interaction. Then, I will compare HFB calculations with the semiclassical local-density approximation. I will show that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms and at zero temperature the two calculations are in good agreement; this agreement is deteriorated at nonzero temperature, especially near the critical temperature.