Scattering-model calculation of the impurity-induced dephasing relaxation rates of the Raman-activeJ=2 rotons in solid parahydrogen

The dephasing relaxation of the J=2 Raman-active ‖k‖≊0 rotons in solid p-${\mathrm{H}}_2$ induced by o-${\mathrm{H}}_2$ impurities is described as elastic scattering of the rotons by these point defects into k≠0 rotons with equal energy. The specific rotational properties of the impurities and the intermolecular interactions between the impurity and the host molecules are not involved in the model calculation: It is argued that the defect can be represented by an empty site in the crystal, leaving the other intermolecular interactions unaltered. The total scattering rate is obtained from a detailed Brillouin zone integration of the golden-rule-type scattering probabilities. The results for the ‖M‖=0 and 1 Raman-active J=2 rotons are very close to the experimental values determined from the linear increase of the dephasing relaxation rates, $T_2^{\mathrm{-}1}$, as a function of o-${\mathrm{H}}_2$ concentration. However, the calculated results for the ‖M‖=2 transition are too small by more than an order of magnitude. The origin of this discrepancy is discussed and possible refinements of the calculation are suggested.