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

TL;DR

This paper calculates localized single-particle potentials for all octet baryons in finite nuclei using SU6 quark-model interactions, providing insights into hyperon behavior and potential for hypernuclear states.

Contribution

It offers a unified SU6 quark-model approach to baryon-baryon interactions, predicting hyperon potentials in finite nuclei with less ambiguity than previous models.

Findings

Sigma potential is weakly attractive at the surface and repulsive inside.

Xi potential is attractive at the surface and fluctuates around zero inside.

Xi hypernuclear bound states are unlikely.

Abstract

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.