  Various theories beyond the Standard Model predict new particles with masses
in the sub-eV range with very weak couplings to ordinary matter. A $P$-odd,
$T$-odd, spin-dependent interaction between polarized and unpolarized matter is
one such possibility. Such a monopole-dipole interaction can be induced by the
exchange of spin-$0$ particles. The presence of a possible monopole-dipole
interaction between fermion spins and unpolarized matter would cause an
decreased transverse spin relaxation time $T_{2}$ for a confined gas of
polarized nuclei. By reanalyzing previously existing data on the spin
relaxation times of polarized $^3$He in gas cells with pressure in the millibar
range and applying the well-established theory of spin relaxation for magnetic
field gradients to gradients in a possible monopole-dipole field, we present
new laboratory constraints on the strength and range of such an interaction.
These constraints represent to our knowledge the best limits on such
interactions for the neutron with ranges between $0.01$ cm and 1 cm.
