Dilute Bose gases interacting via power-law potentials

Neutral atoms interact through a van der Waals potential which asymptotically falls off as r⁻⁶. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parametrize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schrödinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as r⁻⁴.