Three-body scattering hypervolume for bosons with two-body repulsive Gaussian potentials

It has been known that the three-boson low energy effective interaction influences the dynamic and the static properties of many bosons, including the ground state energy of a dilute Bose-Einstein condensate. The three-body scattering hypervolume, which is a three-body analogue of the two-body scattering length, characterizes this effective interaction. For bosons with two-body repulsive Gaussian potentials, we determine the scattering hypervolume by solving the three-body Schr\"{o}dinger equation numerically, and matching the solution with the asymptotic expansions for the wave function at large hyperradii.