Effect of the lattice vibrations on the rotational excitations in solid hydrogen

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Abstract
The theory of the interaction between the lattice vibrations and the rotational excitations in solid H2 is developed using the self-consistent harmonic phonon model with short-range correlations. First- and second-order perturbations in the roton energy levels are calculated using the expansion of the roton–phonon interaction in terms of the quantum-crystal phonon operators derived in a previous paper. The first-order reduction of the quadrupolar coupling constant due to the difference of the longitudinal and transverse sound velocities is calculated and compared with the effect of the short-range correlations. Second-order shifts due to the modulation of the crystalline field and the quadrupolar interactions by the lattice vibrations are also calculated using an isotropic model for the rotons. The roton self-energy shifts are expressed in terms of an effective quadrupolar coupling constant and the dependence of this constant on the roton wave vector is studied. The coupling constant is shown to be appreciably different for propagating and localized rotational excitations.

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