Separable-potential three-body model of theA=6system. II.Li6ground state

Separable-potential three-body ($\alpha \mathrm{np}$) models of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground state are examined. Different separable-potential fits to the $\alpha -n$ phase shifts and the low-energy ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ two-nucleon parameters are reviewed, after which integral equations are derived for the spectator functions of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground-state wave function assuming $S_{\frac{1}{2}}$, $P_{\frac{1}{2}}$, and $P_{\frac{3}{2}}$ components in the $\alpha -n$ interaction. These equations are solved to determine the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ binding energy and investigate its sensitivity to the ${}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ component of the two-nucleon interaction, its variation upon neglecting different components of the $\alpha -n$ interaction, and its dependence on different analytical forms for the $P$-wave $\alpha -n$ interactions. For two wave functions derived from the same set of $\alpha -n$ interactions, but with the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ two-nucleon interaction producing 0% and 4% $d$-wave components in the deuteron, respectively, the spectator functions are given and the contributions to the ground-state normalization of the various components are calculated. The latter two wave functions correspond to three-body ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ binding energies of 4.446 MeV (0%) and 4.070 MeV (4%) compared with the Coulomb-adjusted experimental value of 4.53 MeV.