When does the Tamura model of phonon-isotope scattering break down?

A standard approach to the phonon-isotope scattering problem is the Tamura model [1]. This non-self-consistent 1st Born approximation of the scattering T-matrix expansion is exact for the low energy phonons, and higher order perturbative corrections for the higher energy, dispersive acoustic phonons have been argued to be small [1]. To our knowledge, the validity of this approach for the optic phonons has not yet been demonstrated. In this talk, we compare the Tamura model to the ab initio computed non-perturbative phonon-isotope scattering T-matrix for a set of well-studied materials. We show under what conditions the Tamura model breaks down.

[1] Tamura, S. I. (1983). Isotope scattering of dispersive phonons in Ge. Physical Review B, 27(2), 858.