Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes*

Abstract

Abstract The in-medium feature of nuclear force, which includes both nucleon-nucleon ( ) and hyperon-nucleon ( ) interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new effective interaction in the covariant density functional (CDF) theory, namely, DD-LZ1- , is obtained by fitting the experimental data of Λ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of the Λ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei, and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium interactions and core polarization effects.