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, $phi_{V_5} = [2.8pm,4.6(stat.)pm,4.0(sys.)]times 10^{-5}~mbox{rad/m}$ 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.
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