THEORY OF CRYSTAL-FIELD INTERACTIONS IN SOLID HYDROGEN .1. SINGLE ORTHO IMPURITIES IN SOLID PARA-HYDROGEN

The theory of the crystal-field splitting, V//c, of the J equals 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//c 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 he 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 in the phonon variables. This self-energy effect is calculated using a generalized Debye model for the self-consistent harmonic phonons. The remaining uncertainties in the anisotropic pair potential and the phonon renormalization factors are discussed in connection with the available experimental data.