Three-body problem with separable potentials: (I) bound states

Abstract

The nuclear 3-body problem in which two particles are identical is investigated, by assuming separable potentials to operate between pairs. The separable interactions between n-p pairs have been taken of the types (1) central s-state and (2) tensor (s and d-states); the corresponding n-n interaction is taken to be in the s-state only. For both these cases the exact wave function of the bound 3-nucleon system is obtained in a particularly elegant form which admits of a simple physical interpretation and is easily amenable to mathematical treatment for applications in nuclear physics at low energies. As an application of the formalism, an approximate calculation of the ground state energy of the triton has been carried out by treating the Schrödinger equation as a direct eigenvalue problem without resort to variational techniques, for the case of pure s-state interactions between all the pairs (with parameters adjusted to fit the low-energy singlet and triplet nucleon-nucleon data). The binding energy so obtained is rather close to the actual value.