  We calculate level densities and pairing gaps for an ultracold dilute gas of
fermionic atoms in harmonic traps under the influence of mean field and
anharmonic quartic trap potentials. Super-shell structures, which were found in
Hartree-Fock calculations, are calculated analytically within periodic orbit
theory as well as from WKB calculations. For attractive interactions, the
underlying level densities are crucial for pairing and super-shell structures
in gaps are predicted.
