On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

Abstract

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k0, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k2, two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.