Theory of crystal-field interactions in solid hydrogen. I. Single ortho impurities in solid parahydrogen

Abstract

The theory of the crystal-field splitting, V_e, of the J = 1 level of an ortho impurity in a parahydrogen matrix, due to the coupling of the rotational motion of the ortho molecule to the lattice vibrations, is developed taking due account of the quantum-crystal nature of the solid. Two contributions to V_e are identified, both arising from the anisotropy in the lattice vibrations. One contribution is due to the difference in the relative zero-point motion of the molecules in in-plane and out-of-plane pairs in the hcp lattice, and is parametrized in terms of the second moments of the pair distribution function. The other contribution is due to the local, quasi-state distortion of the lattice around the impurity induced by the terms in the coupling linear in the phonon variables. This self-energy effect is calculated using a generalized Debye model for the self-consistent harmonic phonons, in which the anisotropy of the velocity and of the polarization of the sound waves is parametrized in terms of the elastic constants of the crystal. The theory is compared with that of Raich and Kanney, which is shown to be based on unrealistic assumptions. The remaining uncertainties in the anisotropic pair potential and the phonon renormalization factors are discussed in connection with the available experimental data.