Shell structure of theA=6ground states from three-body dynamics

Abstract

Three-body ($\ensuremath{\alpha}\mathrm{NN}$) models of the $^{6}\mathrm{He}$ and $^{6}\mathrm{Li}$ ground states are used to investigate their shell structure. Three models for each nucleus are considered: simple, full ($\mathrm{nn}$), and full ($\mathrm{np}$) for $^{6}\mathrm{He}$, and simple, full (0%), and full (4%) for $^{6}\mathrm{Li}$. The full models in both cases are obtained by including the ${S}_{\frac{1}{2}}$, ${P}_{\frac{1}{2}}$, and ${P}_{\frac{3}{2}}$ partial waves of the $\ensuremath{\alpha}N$ interaction, whereas the simple model truncates to only the strongly resonant ${P}_{\frac{3}{2}}$ wave. The $^{6}\mathrm{He}$ full models distinguish between use of the $\mathrm{nn}$ or $\mathrm{np}$ parameters for the $^{1}S_{0}$ $\mathrm{NN}$ interaction, while the $^{6}\mathrm{Li}$ full models have either a pure $^{3}S_{1}$ $\mathrm{NN}$ interaction (0%) or a $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ interaction that leads to a 4% $d$-wave component in the deuteron (4%). These models are used to calculate the probabilities of the orbital components of the wave functions, the configuration-space single-particle orbital densities, and the configuration-space two-particle wave function amplitudes in $j\ensuremath{-}j$ coupling with the nucleon coordinates referred to the alpha particle as the "core" or "center of force." The results are then compared with those from phenomenological and realistic-interaction shell models. Major findings of the comparison are the following: None of the shell models considered have a distribution of orbital probabilities across shells like that predicted by three-body models; the orbital rms radii from three-body models indicate an ordering of the orbits within shells, i.e., ${p}_{\frac{1}{2}}$ outside ${p}_{\frac{3}{2}}$, unlike oscillator shell models with a single oscillator parameter where the $p$-shell orbitals have the same shape; and, as expected, three-body orbital densities decay at large radial distances as exponentials rather than the too compact Gaussian falling off of oscillator shell models.NUCLEAR STRUCTURE $^{6}\mathrm{He}$ and $^{6}\mathrm{Li}$, three-body models, shell structure.