Bose-Einstein condensation was realized in dilute gases of Alkali metals and Hydrogen atoms. The scattering length can take a positive or negative value by a subtle change of parameters even if the atomic interaction is always the attractive Van der Waals potential. The scattering length determines the effective interaction in BECs, i.e., the effective interaction is attractive (repulsive) when the scattering length is negative (positive). In this paper, we propose a model system in which the atomic interaction potential obeys a repulsive power law in the long range, and obtain the expression of the scattering length of this model analytically.
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