Low-temperature nuclear-spin relaxation times and line shapes for Hsub2in solid nonmagnetic hosts

We calculate the nuclear-spin relaxation time $T_1$ and line-shape function for isolated ortho- (J=1) ${\mathrm{H}}_2$ molecules in solid nonmagnetic hosts located at sites with various crystal-field symmetries. This work includes modifications of earlier work so that the formalism can be used in regimes where ${\Gamma }_m$, the molecular angular momentum relaxation rate, is not large compared to the molecular-nuclear spin coupling constants ${\omega }_c$ and ${\omega }_d$. The formalism also allows for a nonzero value of the quadrupolarization 〈3$J_z^2$-$J^2$〉. With these changes the theory can be used at temperatures at and below about 4 K where line shapes evolve from Lorentzians into Pake doublets.