Department of Physics Papers

Document Type

Journal Article

Date of this Version

10-15-1971

Publication Source

Physical Review B

Volume

4

Issue

8

Start Page

2781

Last Page

2807

DOI

10.1103/PhysRevB.4.2781

Abstract

The effects of interactions between the elementary excitations (librons) in the orientationally ordered phase of solid H2 and D2 are studied using diagrammatic perturbation theory. This formulation leads naturally to the construction of a renormalized dynamical matrix which includes all anharmonic effects. The cubic anharmonic interactions are by far the dominant ones, and we have calculated the energy shifts of each of the zero-wave-vector libron modes self-consistently to lowest order in the expansion parameter 1/z, where z=12 is the number of nearest neighbors. We find the libron energies (in units of the electrostatic quadrupole-quadrupole coupling constant Γ) to be 11.29 (13.66), 14.07 (17.72), and 19.55 (29.04) with the corresponding harmonic values in parentheses. In contrast to the harmonic theory, these anharmonic results provide a striking fit to the observed Raman spectrum of solid H2 and D2 with reasonable values of Γ, e.g., Γ=0.59 cm−1 for H2 and Γ=0.83 cm−1 for D2. We develop an expression for the Raman intensities in terms of the single-libron spectral weight function. The group-theoretical simplifications in our calculations are discussed in detail in the appendices. The cubic anharmonicity is shown in the accompanying paper to lead to a two-libron spectrum which explains the appearance of "extra" high-energy lines in the Raman spectrum of solid hydrogen. These effects are shown to be included in the renormalized dynamical matrix in the present approximation. Sum rules for the Raman intensities are derived and are used to check the calculations.

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Date Posted: 12 August 2015

This document has been peer reviewed.