The three-body problem is reconsidered using separable potentials for the two-body interactions. Using the separable approximation, the Faddeev equations reduce to coupled integral equations in one continuous variable. The separable two-body interactions used are taken as consisting of two parts to include both attraction and repulsion. Each part of the potential is a spin-dependent central force together with tensor forces. Numerical calculations for the resulting integral equations are carried out to calculate the binding energies of the nuclei ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, using separable potentials of the Yamaguchi, Tabakin, Mongan, and Reid forms. The present calculations show the validity of the separable approximation and that the separable potentials extract accurate binding energies.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; three-body model. Calculated binding energies.

• Received 10 May 1978

DOI:https://doi.org/10.1103/PhysRevC.19.1127