We present a formal derivation of the mean-field expansion for dilute
Bose-Einstein condensates with two-particle interaction potentials which are
weak and finite-range, but otherwise arbitrary. The expansion allows for a
controlled investigation of the impact of microscopic interaction details
(e.g., the scaling behavior) on the mean-field approach and the induced
higher-order corrections beyond the s-wave scattering approximation.Comment: 6 pages of RevTex4; extended discussion, added reference