Absorption intensities of multipole-field-induced double transitions involving orthohydrogen pairs in a solid parahydrogen crystal

Orthohydrogen molecules exhibit quantum diffusion through a solid parahydrogen lattice. At very low orthohydrogen concentrations $(\sim 1\%)$, stable and isolated ortho-${\mathrm{H}}_2$ pairs are formed in the para-${\mathrm{H}}_2$ crystal. In this paper, theoretical expressions are derived for the integrated absorption coefficients of various multipole-field-induced zero-phonon double transitions in an isolated pair of ortho-${\mathrm{H}}_2$ molecules embedded in para-${\mathrm{H}}_2$ crystal. Although, the double transitions involving ortho-${\mathrm{H}}_2$ pairs consist entirely of fine structures (FS), the intensity formulas derived here are for the line as a whole, except for $Q_{v_1}\left(1\right)+Q_{v_k}\left(1\right)$ transition in which the individual components are separately treated. Since the $J=1$ rotational state pair splittings of various ground state FS components are well known, experimentalists can compare the observed intensities to the theoretical calculations for the line as a whole (given in units of per molecular-pair) by reducing the observed intensities of each FS components to per molecular pair and summing them together. The formulas given in this paper can be applied to double transitions involving a pair of $J=1$ dopant molecules (with zero permanent dipole moment) embedded in solid parahydrogen (or orthodeuterium) matrices. Furthermore, it is shown that the intensity formulas given for an isolated pair, after generalization, provide good estimates of the intensities of double transitions in a nearly pure ortho-${\mathrm{H}}_2$ crystal.