Effectives- andp-wave contact interactions in trapped degenerate Fermi gases

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Abstract
The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an effective contact interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multicomponent Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.
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