LocalizedN,Λ,Σ, andΞsingle-particle potentials in finite nuclei calculated withSU6quark-model baryon-baryon interactions

Abstract

Localized single-particle potentials for all octet baryons, $N$, $\ensuremath{\Lambda}$, $\ensuremath{\Sigma}$, and $\ensuremath{\Xi}$, in finite nuclei, $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ca}$, $^{56}\mathrm{Fe}$, and $^{90}\mathrm{Zr}$, are calculated using the quark-model baryon-baryon interactions. $G$ matrices evaluated in symmetric nuclear matter in the lowest order Brueckner theory (LOBT) are applied to finite nuclei in local density approximation. Nonlocal potentials are localized by a zero-momentum Wigner transformation. Empirical single-particle properties of the nucleon and the $\ensuremath{\Lambda}$ hyperon in a nuclear medium have been known to be explained semiquantitatively in the LOBT framework. Attention is focused in the present consideration on predictions for the $\ensuremath{\Sigma}$ and $\ensuremath{\Xi}$ hyperons. The unified description for the octet baryon-baryon interactions by the ${\mathrm{SU}}_{6}$ quark model enables us to obtain less ambiguous extrapolation to the $S=\ensuremath{-}1$ and $S=\ensuremath{-}2$ sectors based on the knowledge in the $\mathit{NN}$ sector than other potential models. The $\ensuremath{\Sigma}$ mean field is shown to be weakly attractive at the surface, but turns out to be repulsive inside, which is consistent with the experimental evidence. The $\ensuremath{\Xi}$ hyperon s.p. potential is also attractive at the nuclear surface region, and inside it fluctuates around zero. Hence $\ensuremath{\Xi}$ hypernuclear bound states are unlikely. We also evaluate energy shifts of the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ and ${\ensuremath{\Xi}}^{\ensuremath{-}}$ atomic levels in $^{28}\mathrm{Si}$ and $^{56}\mathrm{Fe}$, using the calculated s.p. potentials.