Localized $N, \Lambda, \Sigma$, and $\Xi$ Single-Particle Potentials in Finite Nuclei Calculated with $SU_6$ Quark-Model Baryon-Baryon Interactions

Localized single-particle potentials for all octet baryons, $N$, $\Lambda$, $\Sigma$, and $\Xi$, 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 $\Lambda$ 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 $\Sigma$ and $\Xi$ 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 $\Sigma$ 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 $\Xi$ hyperon s.p. potential is also attractive at the nuclear surface region, and inside fluctuates around zero. Hence $\Xi$ hypernuclear bound states are unlikely. We also evaluate energy shifts of the $\Sigma^-$ and $\Xi^-$ atomic levels in $^{28}$Si and $^{56}$Fe, using the calculated s.p. potentials.