Theory of spinor Fermi and Bose gases in tight atom waveguides

The divergence-free pseudo-potentials for spatially even- and odd-wave interactions in spinor Fermi gases in tight atom waveguides were discussed. It was found that the Fermi-Bose method was used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. It was suggested that depending on the relative magnitude of the even- and odd-wave interactions, the N-atom ground state had total spin S=0, S=N/2 and also the intermediate values. Analysis shows that an external magnetic field with a longitudinal gradient caused a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of S_z.