Three-Body Problem with Local Hard-Core Potential

The Faddeev formalism is used to compute the ground-state energy of the triton for a simple model in which the nucleon-nucleon force is given by a spin-independent $s$-wave Herzfeld potential (hard core with outside square well). The effective nucleon-nucleon potential used corresponds to the usual weighted average of triplet and singlet potential strengths. The two-variable Faddeev equation is solved using the complete off-shell $t$ matrix given by: (1) an exact analytic expression, and (2) an integral-equation formalism recently proposed. Three-body calculations based on both evaluations of the two-body $t$ matrix lead to a triton binding energy of 8.13 MeV with about 0.5% accuracy.