Velocity redistribution by standing waves

This paper considers the modifications of the atomic velocity distribution imposed by a standing wave. The recoil due to induced and spontaneous processes provides an effective force on the particles. We formulate the general problem of a two-level atom in the field of two counter-propagating waves. We derive the rate equation limit for these equations and show how it can be generalized to treat a broad-band source of radiation. The connection with generalized relaxation theory is discussed. The ensuing integral equations are solved numerically for various cases of cooling and heating.