Anharmonic Self-Energy of Phonons: Ab Initio Calculations and Neutron   Spin Echo Measurements
  We have calculated (ab initio) and measured (by spin-echo techniques) the anharmonic self-energy of phonons at the X-point of the Brillouin zone for isotopically pure germanium. The real part agrees with former, less accurate, high temperature data obtained by inelastic neutron scattering on natural germanium. For the imaginary part our results provide evidence that transverse acoustic phonons at the X-point are very long lived at low temperatures, i.e. their probability of decay approaches zero, as a consequence of an unusual decay mechanism allowed by energy conservation. 
A. Debernardi (1), F. de Geuser (2), J. Kulda (2), M.Cardona (3), and   E.E.Haller (4) ((1)Istituto Nazionale per la Fisica ...