Mean-Field Expansion in Bose-Einstein Condensates with Finite-Range Interactions

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.