Abstract
The self consistent (SC) theory of lattice dynamics for highly anharmonic crystals is derived via expansion and selected re-summation of the one phonon Green function. Since perturbation treatments of weakly anharmonic crystals use the same expansion, the two cases can then be viewed as variations in a single method. The SC theory to lowest (SCH) and second (SC2) order and a re-order potential power series in which each coefficient appears averaged over the vibrational motion is derived.The SCH theory with the leading correction in the new series, the cubic anharmonic term, is applied to b.c.c. 3He. Phonon frequency dispersion curves, lifetimes, sound velocities, and elastic constants are computed. The phonons are well defined and the elastic constants and isotropy agree quite well with experiment. Although the cubic correction is significant, it suggests that the re-ordered series converges.
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