Three-Body Systems with Square-Well Potentials in L = 0 States

Abstract.

The angular part of the Faddeev equations is solved analytically for s-states in case of two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles, and two identical spin- fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to short-range potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where, for example, large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving in computational efforts could be substantial.