  Shell effects in the coordinate space can be seen with degenerate Fermi
vapors in non-uniform trapping potentials. In particular, below the Fermi
temperature, the density profile of a Fermi gas in a confining harmonic
potential is characterized by several local maxima. This effect is enhanced for
"magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In
the case of a multi-component Fermi vapor, the separation of Fermi components
in different spatial shells (phase-separation) depends on temperature, number
of particles and scattering length. We derive analytical formulas, based on
bifurcation theory, for the critical density of Fermions and the critical
chemical potential, which give rise to the phase-separation.
