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

Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Cross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.