Localized $N,\hat{I}›,\hat{I}\pounds$, and $\hat{I}ž$ Single-Particle Potentials in Finite Nuclei Calculated with $S{U}_6$ Quark-Model Baryon-Baryon Interactions

Abstract

Localized single-particle potentials for all octet baryons, $N$, $\hat{I}›$, $\hat{I}\pounds$, and $\hat{I}ž$, in finite nuclei, ${}^{12}$C, ${}^{16}$O, ${}^{28}$Si, ${}^{40}$Ca, ${}^{56}$Fe, and ${}^{90}$Zr, are calculated using the quark-model baryon-baryon interactions. $G$-matrices evaluated in symmetric nuclear matter in the lowest order Brueckner theory are applied to finite nuclei in local density approximation. Non-local potentials are localized by a zero-momentum Wigner transformation. Empirical single-particle properties of the nucleon and the $\hat{I}›$ hyperon in nuclear medium have been known to be explained semi-quantitatively in the LOBT framework. Attention is focused in the present consideration on predictions for the $\hat{I}\pounds$ and $\hat{I}ž$ hyperons. The unified description for the octet baryon-baryon interactions by the SU${}_6$ quark-model enables us to obtain less ambiguous extrapolation to the $S=-1$ and $S=-2$ sectors based on the knowledge in the $NN$ sector than other potential models. The $\hat{I}\pounds$ mean field is shown to be weakly attractive at the surface, but turns to be repulsive inside, which is consistent with the experimental evidence. The $\hat{I}ž$ hyperon s.p. potential is also attractive at the nuclear surface region, and inside fluctuates around zero. Hence $\hat{I}ž$ hypernuclear bound states are unlikely. We also evaluate energy shifts of the $\hat{I}{\pounds }^{-}$ and $\hat{I}{ž}^{-}$ atomic levels in ${}^{28}$Si and ${}^{56}$Fe, using the calculated s.p. potentials.