Faddeev treatment of ⁶Li with a separable potential

Abstract

The nucleus ⁶Li, together with its first excited state ⁶Li^*, is treated as a three-body problem consisting of an a particle, a proton, and a neutron, interacting through separable potentials in pairs. The N-N potential includes a tensor force in addition to a central (S-wave) term of the Yamaguchi type. The p-wave part of the α-N potential is parametrized in terms of the sum of a central and a small spin-orbit term which fits the experimental P_3/2 and P_1/2α-N phase shifts quite accurately. The smallness of the spin-orbit part justifies its omission from the full three-body equations. The binding energies and the wave functions for the ground (J^P=1⁺) and excited (J^P=0⁺) states of ⁶Li are calculated by solving the coupled Faddeev equations numerically. The calculated binding energy for the 1⁺ state is a little higher than, and that for the 0⁺ state a little lower than, the corresponding experimental values, corrected for Coulomb effects.