The spatial and momentum distributions of a weakly interacting Fermi gas trapped in an external potential

The spatial and momentum distributions of a weakly interacting Fermi gas trapped in a spherical symmetric power-law potential are investigated, based on the mean field approximation. The concepts of “Fermi spheres” in both the coordinate and momentum spaces are introduced and the problem of how the sizes of the “Fermi spheres” depend on the external potential and interatomic interaction is discussed. Density profiles in both spaces are presented explicitly and the effects of the external potential, interatomic interaction and temperature on the spatial and momentum distributions are shown clearly. The results obtained are general because the power-law potential adopted here may include a variety of particular potentials corresponding to the various values of the exponents.