Density-dependent relativistic mean-field model for $ \Xi^{-} $ hypernuclei

In hypernuclear systems, interactions involving nucleons and hyperons are intricately influenced by the surrounding particles, particularly by the density and the isospin feature of the nuclear medium. In this work, the relativistic mean-field (RMF) theory is adopted to describe the structure of several typical $\Xi^{-}$ hypernuclei. New sets of $\Xi N$ effective interactions, by taking a density-dependent meson-nucleon/hyperon coupling perspective, are developed by fitting experimental data on the $\Xi^{-}$ hyperon $1s$ and $1p$ state separation energy of $^{15}_{\Xi^{-}}$C as well as the $1p$ state separation energy of $^{13}_{\Xi^{-}}$B. The density-dependent behavior of meson-hyperon coupling strengths sensitively affects the description of hyperon single-particle levels. In fact, the density-dependent meson-baryon coupling strengths introduce additional rearrangement contributions to the hyperon self-energy. Correspondingly, detailed forms of density dependence in these coupling strengths and different considerations of meson-baryon coupling channels will impact the hyperon single-particle properties within hypernuclei. Especially with the additional inclusion of the isovector scalar $\delta$ meson, the significant enhancement of rearrangement terms in the effective interaction DD-ME$\delta$ impacts the shape of the hyperon potential and alters the characteristics of the isovector channel dynamics balance in the effective nuclear force. Relevant research underscores the importance of precisely accounting for in-medium effects in hyperon-nucleon interactions and incorporating a more comprehensive set of meson-exchange degrees of freedom in effective nuclear forces, offering a potential solution for more self-consistently describing the featured hyperon single-particle behavior of various hypernuclei and for reducing uncertainties in theoretical descriptions.