Anharmonic phonon shifts and widths for a centro symmetrical potential

Abstract

The anharmonic effects to lowest nonvanishing order, such as the shift and broadening of the one phonon neutron scattering peaks, in inert-gas solids have been calculated numerically. Approximations in the treatment have been avoided. The potential model employed is the LennardJones[6, 12] centro symmetrical potential, and interactions beyond third neighbour shells have been neglected. The calculation has been simplified by using the law of corresponding states, introducing the quantum parameter Λ ∗ as the only formal difference between different elements. The results are presented in the reduced units of corresponding states. As there, to our knowledge, has been no measurements of phonon widths for inert-gas solids we have also calculated the wave number dependence of phonon widths for aluminum using the Lennard-Jones[6, 12] potential, adjusting the parameters to experimental thermal expansion data. The theoretical widths are compared with the experimental widths reported by Stedman and Nilsson. It must be emphasized that the employed potential of course is a very poor approximation for a metal potential but it might to some extent be excused as it, in this case, reasonably good reproduces the experimental phonon dispersion curves and frequency distribution.