Three-Body Calculations with Local Potentials

A two-term separable approximation to the two-particle $t$ matrix is developed which preserves exact behavior at each bound-state or resonance pole. While introducing no additional singularities, the approximation also produces the exact right-hand cut. This separable approximation is applied to the three-particle scattering problem with local potentials, and numerical results are obtained for the three-body binding energy in the case of the Yukawa and exponential potentials. A prescription is given for increasing the accuracy of this approach by systematically increasing the number of separable terms. This procedure is tested numerically, as is a method for estimating the error in such calculations. Binding-energy results are also presented for a modified pole approximation, and a simple explanation is given for the infinite-binding-energy phenomenon observed by Osborn for separable potentials.