Roton-phonon mixing in solid hydrogen and deuterium

Solid parahydrogen and orthodeuterium have been studied under high pressure in a diamond anvil cell at low temperature. The frequency of the k\ensuremath{\rightarrow}=0 ${E}_{2g}$ transverse-optical phonon increases rapidly with density. In the vicinity of the roton modes it hybridizes with the ${E}_{2g}$ roton resulting in a level anticrossing. The interaction Hamiltonian is analyzed for an (effective) linear coupling between the roton and phonon. Of the two most important contributions to the coupling, the crystal-field interaction B(R) is found to be significantly stronger than the mechanism arising from the electric quadrupole-quadrupole interaction \ensuremath{\Gamma}(R). This enables us to make the first determination of B(R) in the solids at two densities. The resulting experimental potential is significantly smaller than the theoretical pair potential. These measurements provide an important experimental test for theoretical anisotropic potentials.