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A comparison between existing measurements and calculations of the scalarspin-spin interaction (J-coupling) in deuterated molecular hydrogen (HD) yieldsstringent constraints on anomalous spin-dependent potentials between nucleonsat the atomic scale (${\rm \sim 1 \AA}$). The dimensionless coupling constant$g_P^pg_P^{N}/4\pi$ associated with exchange of pseudoscalar (axion-like)bosons between nucleons is constrained to be less than $5\times 10^{-7}$ forboson masses in the range of $5 {\rm keV}$. This represents improvement by afactor of about 100 over constraints placed by measurements of thedipole-dipole interaction in molecular ${\rm H_2}$. The dimensionless couplingconstant $g_A^pg_A^N/4 \pi$ associated with exchange of a heretoforeundiscovered axial-vector boson between nucleons is constrained to be$g_A^pg_A^N/4 \pi < 2 \times 10^{-19}$ for bosons of mass $\lesssim 1000 {\rmeV}$, improving constraints at this distance scale by a factor of 100 forproton-proton couplings and more than 8 orders of magnitude for neutron-protoncouplings. This limit is also a factor of 100 more stringent than recentconstraints obtained for axial-vector couplings between electrons and nucleonsobtained from comparison of measurements and calculations of hyperfinestructure.

Constraints on short-range spin-dependent interactions from scalar spin-spin coupling in deuterated molecular hydrogen