Elastic scattering loss of atoms from colliding Bose-Einstein condensate wave packets

Bragg diffraction of atoms by light waves can create high momentum componen ts in a Bose-Einstein condensate. Collisions between atoms from two distinc t momentum wave packets cause elastic scattering that can remove a signific ant fraction of atoms from the wave packets and cause the formation of a sp herical shell of scattered atoms. We develop a slowly varying envelope tech nique that includes the effects of this loss on the condensate dynamics des cribed by the Cross-Pitaevski equation. Three-dimensional numerical calcula tions are presented for two experimental situations: passage of a moving da ughter condensate through a nonmoving parent condensate, and four-wave mixi ng of matter waves.