The separable-potential approach of Mitra is extended by introducing an additional interaction which yields two-nucleon $S$-wave phase shifts to 340 MeV. A calculation of the exact binding energy and wave function of a simplified three-body system is used to determine the role of short-range correlations and the associated off-energy-shell matrix elements of the interaction. We find that the three-body binding energy ranges from 9.33 to 8.40 MeV; the larger value is calculated using a two-body interaction fitting low-energy data only, while the smaller value results from including a hard-shell repulsion. A smooth repulsion, which is equivalent to the hard shell in the two-body problem, yields a three-body binding energy of 8.79 MeV.

• Received 21 August 1964

DOI:https://doi.org/10.1103/PhysRev.137.B75