Phonon self energy in transition metals

We present \emph{ab initio} calculations of the phonon self energy of transition metals obtained using second order many body perturbation theory.\footnote{S. Narasimhan and D. Vanderbilt, Phys. Rev. B, 43, 4541 (1991)} The code we have implemented\footnote{L. Chaput, A. Togo, I. Tanaka and G. Hug, submitted to Phys. Rev. B} use the symmetry properties of the phonon-phonon interactions to express the self energy as a sum over irreducible triplets. It is analogous to the reduction of integration to the irreducible part of the Brillouin zone for one particle properties. The self energy of transition metals is then calculated. We show that the Peierls approximation\footnote{R. E. Peierls, Quantum Theory of Solids, Oxford University Press,1964} is in fact reasonable for \emph{bcc} and \emph{fcc} metals, but fails for the \emph{hcp}. The decays paths of phonons producing the self energy is finally analyzed using surfaces of reciprocal space defined by conservation law.