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 Gross-Pitaevski equation. Three-dimensional numerical …

Bragg scattering can be used to create a daughter wavepacket with momentum k from a
parent Bose-Einstein condensate, where k is very large compared to the momentum spread
of the parent. Elastic collisions between atoms in the moving wavepacket and atoms in the
parent results in formation of a shell of elastically scattered atoms with momentum k/2 that
are lost from two original wavepackets. We apply a slowly-varying-envelope approximation
to calculate the time-dependent dynamics of the two interacting wavepackets and account …