  Divergence-free pseudopotentials for spatially even and odd-wave interactions
in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose
mapping method is used to relate the effectively one-dimensional fermionic
many-body problem to that of a spinor Bose gas. Depending on the relative
magnitudes of the even and odd-wave interactions, the N-atom ground state may
have total spin S=0, S=N/2, and possibly also intermediate values, the case
S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground
state is space-antisymmetric and spin-symmetric. In this case the fermionic
ground state maps to the spinless bosonic Lieb-Liniger gas. An external
magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial
separation of the corresponding trapped Fermi gas with respect to various
values of $S_z$.
