Separable potential three-body model of the A = 6 system. I. 6He ground state

Separable-potential three-body (αnn) models of the ⁶He ground state are investigated. Different separable-potential fits to the α-n phase shifts and the low-energy singlet two-nucleon parameters are discussed, after which integral equations are derived for the spectator functions of the ⁶He ground-state wave function assuming S_1/2, P_1/2, and P_3/2 components in the α-n interaction. These equations are solved to determine the ⁶He binding energy and examine its sensitivity to the two-nucleon singlet effective range, its variation upon neglecting different components of the α-n interaction, and its dependence on different analytic forms for the P-wave α-n interactions. The spectator functions for the "best" two sets of parameters are generated and tabulated, and for one set the contributions to the ground-state normalization of the various components in the ⁶He ground-state wave function are computed. With the "best" S_1/2,P_1/2, and P_3/2 α-n interactions, the calculated ⁶He binding energy is 0.542 MeV for a two-nucleon s-wave separable potential fitted to the n-p ¹S₀ effective-range parameters, r₀=2.73 fm, and a=-23.715 fm, and 0.359 MeV for the n-n ¹S₀ effective-range parameters, r₀=2.84 fm, and a=-17 fm, compared to the experimental value of 0.969 MeV.[NUCLEAR STRUCTURE ⁶He; calculated binding energy, wave function, contribution of wave function components to normalization. Three-body, separable-potential model.]