Signatures of Bose-Einstein condensation in very low energy atomic scattering from trapped gases

We report wave packet analysis of scattering of identical particles from for a Bose condensed dilute gas trapped in a spherical square well of finite depth, using solutions to the Bogoliubov equations which we previously reported. Simulations show clearly that exchange effects lead to significant amplitudes for passage of the particle through the condensate, a "transparency effect," accounting for the extremely small cross sections previously calculated. The interactions are treated in the scattering length approximation. The states exhibiting enhanced transparency appear to arise from a kind of self stabilizing Ramsauer-Townsend effect. We also observe anomalously large scattering of the identical particles from the condensate for a few other combinations of coupling strength and k vector. We show that these scattering states associated with large cross section are resonance states in which there is a large enhancement of the amplitude of the scattering state in the region of the condensate, corresponding to a state which is nearly bound. We also exhibit simulations of the scattering density at large k, where we previously consistently observed that exchange reduced the cross section. The simulations show enhanced transparency.