Collision-broadened phonon line shape in the overdamped or hydrodynamic regime

It can be shown that if amplitude as well as momentum changes during phonon scattering events are taken into account, the line shape associated with infrared- or Raman-active lattice modes can be of the Lorentz or Van Vleck-Weisskopf form as well as of the damped-oscillator form. An expression is derived for the susceptibility of an active mode of an anharmonic lattice. This expression reduces to the damped-oscillator form in the collisionless regime and to the Van Vleck-Weisskopf form in the collision-dominated regime. It is emphasized that such considerations should be important in the vicinity of a second-order phase transition where an active-mode frequency becomes anomalously low and the mode becomes overdamped. © 1974 The American Physical Society.