INELASTIC-SCATTERING OF PHONONS BY QUADRUPOLE DEFECTS WITH INTERNAL DEGREES OF FREEDOM

We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice for the case of s olid parahydrogen whose matrix contains pair complexes of H-2 orthomol ecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction of the molecules in an orthopair we derive an effective Hamiltonian that describes the inter action of phonons with a pair quadrupole orthodefect in the lattice. W e set up the scattering matrix and calculate the effective phonon rela xation time tau(omega,T) as a function of the frequency w and the crys tal temperature T. We also find that a pair quadrupole defect, which h as a complicated system of levels, can be replaced by an effective two -level system with temperature-dependent parameters. The fact that a p air quadrupole orthocluster has internal degrees of freedom results in a resonant scattering peak near a certain critical temperature To. Ou r estimates for Ha yield T-0 similar or equal to 6-7 K. Finally, we di scuss the contribution of this mechanism to the low-temperature therma l conductivity of solid hydrogen. (C) 1998 American Institute of Physi cs. [S1063-7761(98)01408-5].