Delta-function fermi gas with two-spin deviates

The problem of one-dimensional particles interacting via a delta-function potential has been a useful model for the many-body problem. While it can be solved for bosons, it has so far not been solved for fermions except for the special cases of either all spins parallel or all but one spin parallel. The full difficulty of the problem first manifests itself when two spins are down (i.e., S=12N-2), and this we solve here. We are confident that our method can be extended to the general problem.