  We analyze atom-atom correlations in the s-wave scattering halo of two
colliding condensates. By developing a simple perturbative approach, we obtain
explicit analytic results for the collinear (CL) and back-to-back (BB)
correlations corresponding to realistic density profiles of the colliding
condensates with interactions. The results in the short time limit are in
agreement with the first-principles simulations using the positive-$P$
representation and provide analytic insights into the experimental observations
of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision
durations, we predict that the BB correlation becomes broader than the CL
correlation.
