  We introduce an exactly solvable model of a fermi gas in one dimension and
compute the momentum distribution exactly. This is based on a generalisation of
the ideas of bosonization in one dimension. It is shown that in the RPA
limit(the ultra-high density limit) the answers we get are the exact answers
for a homogeneous fermi gas interacting via a two-body repulsive coulomb
interaction. Furthermore, the solution may be obtained exactly for arbitrary
functional forms of the interaction, so long as it is purely repulsive. No
linearization of the bare fermion dispersion is required. We find that for the
interaction considered, the fermi surface is intact for weak repulsion and is
destroyed only for sufficiently strong repulsion. Comparison with other models
like the supersymmetric t-J model with inverse square interactions is made.
