Interactions between Molecules in Solid Hydrogen

The interactions between molecules in solid ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are discussed with emphasis on those features which are of importance for the orientational properties. It is shown that pseudo-three-body interactions split by 0.1 ${\mathrm{cm}}^{-1\mathrm{}}$ the rotational levels of a pair of $J=1\mathrm{}$ molecules which are degenerate when only pairwise interactions are considered. The dielectric screening of quadrupole interactions due to these terms is also estimated. The static and dynamic renormalizations of the electric quadrupole-quadrupole interaction constant $\Gamma$ due to phonon interactions are studied using the theory of quantum crystals and treating the dynamical interaction between phonons and rotations perturbatively. For ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ in the fcc phase, a reduction in $\Gamma$ of about 12% is found therefrom, where as in the dilute $J=1\mathrm{}$ solid practically no renormalization is expected. By comparing the author's calculations with experimental data, it is infered that perhaps the static renormalization has been underestimated as a result of the crude description of the phonon modes. However, the differing renormalizations for the dilute and concentrated $J=1\mathrm{}$ systems are confirmed by experiment. Finally, the indirect interaction between distant $J=1\mathrm{}$ molecules analogous to the Suhl-Nakamura interaction is discussed. It is shown that the NMR ${\mathrm{T}}_2$ data place a bound on this interaction which can only be understood using rather small values of certain intermolecular interaction coefficients which are renormalized to take account of short-range correlations. Harmonic renormalization leads to anomalously large indirect interactions in disagreement with ${\mathrm{T}}_2$ data.