Phonon-phonon interactions in transition metals

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 ${10}^{\ensuremath{-}10}$ 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.