  We present a search for possible spin dependent interactions of the neutron
with matter through exchange of spin 1 bosons with axial vector couplings as
envisioned in possible extensions of the Standard Model. This was sought using
a slow neutron polarimeter that passed transversely polarized slow neutrons by
unpolarized slabs of material arranged so that this interaction would tilt the
plane of polarization and develop a component along the neutron momentum. The
result for the rotation angle, $\phi'_{V_5} =
[2.8\pm\,4.6(stat.)\pm\,4.0(sys.)]\times 10^{-5}~\mbox{rad/m}$ is consistent
with zero. This result improves the upper bounds on the neutron-matter coupling
$g_{A}^{2}$ from such an interaction by about three orders of magnitude for
force ranges in the mm-$\mu$m regime.
