One-Phonon Spectral Function for Solid Helium

Abstract

Approximate numerical calculations are used in order to understand some of the differences in size and shape of secondary structure obtained in calculations of the one-phonon spectral function for solid helium which have been reported in the literature. It is seen that Horner's self-consistent treatment of the bubble diagram significantly increases the size of such structure over that obtained in perturbative calculations such as used by Glyde and co-workers. A computational procedure used by Horner in evaluating the spectral function may also further enhance the appearance of secondary peaks in the tail region. Previous explanations of these secondary peaks are reviewed and criticised. Other calculations of the onephonon spectral functions for the solid heliums are briefly discussed.

The phonon absorption line shape of solid molecular H2 and D2 as a function of density

“…23 '33-35 They have also been discussed by Leath and Watson, 36 Ruvalds,25 and McMahan and Beck,37 where some controversy has arisen as to the precise origin of the double-peak structure. Ruvalds 25 has proposed that the secondary peak structure in the one-phonon spectral function of anharmonic crystals could be produced by two-phonon bound states and resonances.…”

Far-infrared absorption in solid hydrogen and deuterium in the ordered state as a function of density

“…This implies that even in crystals with a *For a review see, e.g., Ref. 38. moderate anharmonicity, close attention must be paid to the lineshape, which can have a multipeaked structure for a one-phonon response.…”

The effect of anharmonicity on the spectral shape of linear chains

“…Although their calculations were for a non-linear chain only, Leath and Watson have speculated that the additional peak might exist in solid He. MacMahan and Beck [14], on the other hand, have suggested that the subsidiary zone-boundary peaks found by Horner arise from a computational technique alone. Glyde [15] speculates that subsidiary peaks have not so far been observed in the experiments because they may be masked by multiphonon scattering.…”