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

The theory of the crystal-field splitting, V,, of the J = I level of an ortho impurity in a parahydl-ogen 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 contl-ibutions to V, 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 end 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 termsof theelastic constants of the crystal. The theory is compared with that of Raich and Kanney, which is shown to be based on unrealis'iicassumptions. The I-emaining uncertainties in the anisotropic pair potential and the phonon renormalization factors are discussed in connection with the available experimental data.