  Bragg diffraction divides a Bose-Einstein condensate into two overlapping
components, moving with respect to each other with high momentum. Elastic
collisions between atoms from distinct wave packets can significantly deplete
the condensate. Recently Zi\'{n} {\it et al.} (Phys. Rev. Lett. {\bf 94},
200401 (2005)) have introduced a model of two counter-propagating atomic
Gaussian wavepackets incorporating dynamics of the incoherent scattering
processes. Here we study the properties of this model in detail, including the
nature of the transition from spontaneous to stimulated scattering. Within the
first order approximation we derive analytical expressions for the density
matrix and anomalous density which provides excellent insight into correlation
properties of scattered atoms.
