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.Comment: 14 pages, 3 figure
