Alpha-deuteron structure ofLi6as predicted by three-body models

Abstract

Three-body ($\ensuremath{\alpha}\mathrm{NN}$) 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 Schr\"odinger equation with the $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ $n\ensuremath{-}p$ interaction (4% $D$ state in the deuteron) plus the ${S}_{\frac{1}{2}}$, ${P}_{\frac{1}{2}}$, and ${P}_{\frac{3}{2}}$ $\ensuremath{\alpha}\ensuremath{-}N$ interactions, whereas the full (0%) and simple models truncate the $n\ensuremath{-}p$ 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 $\ensuremath{\alpha}\ensuremath{-}N$ interaction. These models are used to calculate the $s$- and $d$-wave $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$ momentum distributions, the percentage of $s$- and $d$-wave $\ensuremath{\alpha}\ensuremath{-}d$ components in the $^{6}\mathrm{Li}$ wave functions, the effective $s$- and $d$-wave configuration-space wave functions, and the $S$- and $D$-wave $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$ asymptotic normalization constants. The most sophisticated of the models, full (4%), predicts a $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$ momentum distribution in agreement at low momentum transfers ($q\ensuremath{\lesssim}0.3$ ${\mathrm{fm}}^{\ensuremath{-}1}$) with the latest momentum distribution extracted from a 670 MeV $^{6}\mathrm{Li}(p,pd)\ensuremath{\alpha}$ experiment; a 65.4% $\ensuremath{\alpha}\ensuremath{-}d$ 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 $\ensuremath{\alpha}\ensuremath{-}d$ wave functions have nodes at \ensuremath{\sim}1.6 and \ensuremath{\sim}1.65 fm, respectively, though they differ in shape; and the values of the $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, $S$- 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 $n\ensuremath{-}p$ tensor force and repulsive ${S}_{\frac{1}{2}}$ $\ensuremath{\alpha}\ensuremath{-}N$ interaction. The character of the $\ensuremath{\alpha}\ensuremath{-}d$ $d$-wave component is thoroughly examined.NUCLEAR STRUCTURE $^{6}\mathrm{Li}$, three-body models, asymptotic norms, spectroscopic factors, momentum distributions.