Elastic constants and anisotropic pair correlations in solid hydrogen and deuterium

Abstract

The anisotropic displacement–displacement correlation function for the two types of pairs of nearest neighbours in solid hep hydrogen and deuterium is studied. Two mechanisms contributing to the deviation of the pair distribution function from axial symmetry around the pair axis are identified. The one is due to the anisotropy of the phonon dispersion relations and is treated in a generalized Debye model parameterized in terms of the elastic constants. The elasticity tensor is decomposed into rotationally irreducible parts, and certain new relations between the elastic constants of hep crystals with central forces are derived. The other mechanism arises from the immediate, anisotropic environment of a pair and is treated using a generalized Einstein model. The relevance of these results for the interpretation of the microwave spectrum of pairs of orthohydrogen molecules in parahydrogen is also discussed.