Distribution function for the orientational order parameters in solid H2 and D2

A model for the distribution function P(σ,η) for the axial and eccentric orientational order parameters σ and η is proposed for a system of quadrupoles which represents the situation in solid H2 and D2. It is based on a plausible approximation to the exact one-particle orientational density matrix for J=1 molecules in the randomly distributed (J=1)X(J=0)(1-X) solid, where X is the molar concentration of the J=1 component. The properties of P(σ,η) are described, and can be expressed as a function of a single parameter D. Three-dimensional representations of P(σ,η) for several values of D are shown, where D≪1 and D≫1 represent the extreme situations for zero and complete ordering. By means of the P(σ,η) model, the NMR line shape for an ortho-para-mixture polycrystalline sample is calculated and compared with experiments in H2. The correlation of the parameter D with a given ordering state in the temperature-concentration plane for H2, the effect of zero-point motion, and the effect of crystalline anisotropy on the line shape are discussed.