Self-Consistent Phonon Theory

Abstract

Abstract The self-consistent phonon (SCP) theory is an elegant and pragmatic method for evaluating the dynamics of atoms in anharmonic crystals. In it, anharmonic contributions are summed into a generalized force constant. It is particularly suited to solid helium since, as noted in Chapter 3, the harmonic approximation (HA) is very poor and anharmonic terms are large. Also, the He–He interatomic potential has a steeply repulsive hard core. This makes the quartic and higher even anharmonic terms, that are summed in the lowest order SCP theory, larger than the cubic anharmonic term which appears first in second order. Thus the lowest order SCP theory, denoted the self–consistent harmonic (SCH) approximation, already provides a reasonable description of the phonon energies. This is not the case in alkali metals, for example, where the quartic and cubic anharmonic terms make approximately equal and opposite contributions. The SCH theory applied to solid helium is reviewed by Koehler (1975), Horner (1974a), Varma and Werthamer (1976), Glyde (1976), and Werthamer (1976).