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New particles with masses in the sub-eV range have been predicted by varioustheories beyond the Standard Model. Some can induce new spin-spin interactionsbetween fermions. Existing constraints on such interactions between nucleonswith mesoscopic ranges (millimeters to nanometers) are quite poor. Polarized$^{3}$He gas is an especially clean system to use to constrain these possiblenew spin-spin interactions because the spin-independent atomic potentialbetween helium atoms is well-characterized experimentally. The small effectsfrom binary atomic collisions in a polarized gas from magnetic dipole-dipoleand other possible weak spin-spin interactions which lead to spin relaxationcan be calculated perturbatively. We compare existing measurements of thelongitudinal spin relaxation rate $\Gamma_{1}$ of polarized $^3$He gas withtheoretical calculations and set a $1\sigma$ upper bound on the pseudoscalarcoupling strength $g_p$ for possible new neutron-neutron dipole-dipoleinteractions of $g_p^{(n)}g_p^{(n)}/4\pi \le 1.7\times 10^{-3}$ for distanceslarger than 100 nm. We also set new direct limits on possible gravitationaltorsion interactions between neutrons.

Limits on possible new spin-spin interactions between neutrons from measurements of the Longitudinal Spin Relaxation Rate of Polarized $^{3}$He Gas