  A comparison between existing measurements and calculations of the scalar
spin-spin interaction (J-coupling) in deuterated molecular hydrogen (HD) yields
stringent constraints on anomalous spin-dependent potentials between nucleons
at 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 $5\times 10^{-7}$ for
boson masses in the range of $5 {\rm keV}$. This represents improvement by a
factor of about 100 over constraints placed by measurements of the
dipole-dipole interaction in molecular ${\rm H_2}$. The dimensionless coupling
constant $g_A^pg_A^N/4 \pi$ associated with exchange of a heretofore
undiscovered axial-vector boson between nucleons is constrained to be
$g_A^pg_A^N/4 \pi < 2 \times 10^{-19}$ for bosons of mass $\lesssim 1000 {\rm
eV}$, improving constraints at this distance scale by a factor of 100 for
proton-proton couplings and more than 8 orders of magnitude for neutron-proton
couplings. This limit is also a factor of 100 more stringent than recent
constraints obtained for axial-vector couplings between electrons and nucleons
obtained from comparison of measurements and calculations of hyperfine
structure.
