Dephasing relaxation ofJ=2rotons in parahydrogen crystals doped with hydrogen-deuterium impurities

The dephasing relaxation times $T_2$ of the Raman-active J=2 rotons in para-${\mathrm{H}}_2$ crystals, intentionally doped with HD impurities, were measured by means of the time-resolved stimulated-Raman-gain (TRSRG) technique. The relaxation rates $T_2^{\mathrm{-}1}$ corresponding to the spectral linewidth δν=(π$T_2$ ${)}^{\mathrm{-}1}$ are found to increase linearly with HD concentration with the slopes 0.148±0.05 ${\mathrm{cm}}^{\mathrm{-}1}$, 0.126±0.05 ${\mathrm{cm}}^{\mathrm{-}1}$, and 0.140±0.05 ${\mathrm{cm}}^{\mathrm{-}1}$ per percent for the ‖M‖=0, 1, and 2 rotons, respectively, which, within experimental error, are the same as in the case of ortho-${\mathrm{H}}_2$ impurities. This result demonstrates the equivalence of HD and ortho-${\mathrm{H}}_2$ for scattering of J=2 rotons in para-${\mathrm{H}}_2$. Furthermore the previously suggested possibility that the extrapolated values for the roton relaxation rate in pure para-${\mathrm{H}}_2$ would originate from HD impurities at the natural isotope concentration ($c_{\mathrm{HD}\mathrm{\approxeq }0.03}$%) is eliminated.