Rayleigh scattering from a trapped bose condensate and the corresponding recoil atom velocity distribution

An approach has been developed that allows the Rayleigh scattering cross section to be calculated with allowance for the quantum character of motion of the center of mass of the trapped scattering particles. The shape of the line of light scattering from a Bose condensate in a parabolic trap has been studied. A shift of the scattering line center is equal to the recoil shift, while the line width depends on the chemical potential of the Bose gas and on the relaxation time of the velocity of the above-condensate recoil particles. A velocity distribution function in the beam of recoil atoms formed in the course of induced Rayleigh scattering is determined. It is shown that, under the typical experimental conditions, the characteristic width Δv/v of the recoil velocity distribution in this beam is on the order of 10^?3 at a velocity v on the order of several centimeters per second.