Three-body ($\alpha \mathrm{NN}$) models of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground state are used to examine its alpha-deuteron structure. Three models of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground-state wave function are considered: simple, full (0%), and full (4%). The full (4%) model is derived by solving the Schrödinger equation with the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ $n-p$ interaction (4% $D$ state in the deuteron) plus the $S_{\frac{1}{2}}$, $P_{\frac{1}{2}}$, and $P_{\frac{3}{2}}$ $\alpha -N$ interactions, whereas the full (0%) and simple models truncate the $n-p$ interaction to only the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ component and the simple model also drops the $S_{\frac{1}{2}}$ and $P_{\frac{1}{2}}$ components of the $\alpha -N$ interaction. These models are used to calculate the $s$- and $d$-wave ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$ momentum distributions, the percentage of $s$- and $d$-wave $\alpha -d$ components in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ wave functions, the effective $s$- and $d$-wave configuration-space wave functions, and the $S$- and $D$-wave ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$ asymptotic normalization constants. The most sophisticated of the models, full (4%), predicts a ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$ momentum distribution in agreement at low momentum transfers ($q\lesssim 0.3$ ${\mathrm{fm}}^{-1\mathrm{}}$) with the latest momentum distribution extracted from a 670 MeV ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\mathrm{}(p,pd)\mathrm{}\alpha$ experiment; a 65.4% $\alpha -d$ component in the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ wave function with only 0.049% coming from the $d$-wave contribution; that both the $s$- and $d$-wave effective $\alpha -d$ wave functions have nodes at ∼1.6 and ∼1.65 fm, respectively, though they differ in shape; and the values of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}\to \alpha +d$, $S$- and $D$-wave asymptotic normalization constants to be 2.182 and 0.0178, respectively, consistent with present experimental values. Detailed comparison between the models is made, especially with respect to the role of the $n-p$ tensor force and repulsive $S_{\frac{1}{2}}$ $\alpha -N$ interaction. The character of the $\alpha -d$ $d$-wave component is thoroughly examined.

NUCLEAR STRUCTURE ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, three-body models, asymptotic norms, spectroscopic factors, momentum distributions.

• Received 18 September 1981

DOI:https://doi.org/10.1103/PhysRevC.25.2743