In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be reasonable for bcc and fcc metals. For hcp metals we show that the Raman active mode decays into a pair of acoustic phonons, their wave vector being located on a surface defined by conservation laws.
@article{arxiv.1103.0137,
title = {Phonon-phonon interactions in transition metals},
author = {Laurent Chaput and Atsushi Togo and Isao Tanaka and Gilles Hug},
journal= {arXiv preprint arXiv:1103.0137},
year = {2015}
}