We derive the explicit three-body contact potential for a dilute condensed Bose gas from microscopic theory. The three-body coupling constant exhibits the general form predicted by Wu [Phys. Rev. 115, 1390 (1959)] and is determined in terms of the amplitudes of two- and three-body collisions in vacuum. In the present form, the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few-body collisions and the stability of condensates with attractive two-body forces.

• Received 22 April 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.210404