Optical response of metals in a number-conserving relaxation-time approximation

The electronic transport equations for a periodic solid are presented in a number-conserving relaxation-time approximation. The inclusion of a phenomenological scattering time and the concurrent imposition of the equation of continuity is shown to lead to quantum-mechanical interference between the scattering mechanism and the primary effects of the periodic crystalline field. In model calculations carried out for the simple metals, the consequences of this interference are examined in the context of both optical interband transitions and the damping of the long-wavelength volume plasmons. An interband contribution to the static conductivity is also found as a direct consequence of the conserving approximation. It can be expressed as a relatively simple function of both scattering time and oscillator strengths. Local-field effects are also discussed within the same model.