A beyond-mean-field model for Λ hypernuclei with Skyrme-type NΛ interaction

Abstract

A beyond-mean-field approach based on the Skyrme–Hartree–Fock model is derived and implemented for $^{13}_{\ \,\Lambda}$C and $^{21}_{\ \Lambda}$Ne. The Skyrme force with the SLy4 parameter set is used for $NN$ interaction, and a recently updated Skyrme-type parameter set, SLL4, is employed for $N\Lambda$ interaction. The hyperonic spin–orbit force is also included to reproduce the spin–orbit splitting of single-particle energy levels and the no-crossing rule. Properties of different configurations, such as $^{12}$C$\otimes\Lambda[000]1/2^+$, $^{12}$C$\otimes\Lambda[110]1/2^-$, $^{12}$C$\otimes\Lambda[101]3/2^-$, and $^{12}$C$\otimes\Lambda[101]1/2^-$ are discussed. Low-lying energy spectra of $^{13}_{\ \,\Lambda}$C, including both positive- and negative-parity levels, are presented and compared to the observed data. It is shown that this current model precisely reproduces the observed positive-parity energy level with the configuration [$^{12}C_{\textrm{g.s.}}(2^+)\otimes s_\Lambda$]. The two observed negative-parity levels, [$^{12}C_{\textrm{g.s.}}(0^+)\otimes(p_{1/2})_\Lambda$] and [$^{12}C_{\textrm{g.s.}}(0^+)\otimes(p_{3/2})_\Lambda$], are also successfully reproduced but with reversed order. Energy spectra of $^{21}_{\ \Lambda}$Ne are also presented and compared to the results of a beyond relativistic mean-field model; except for some details, the two models give similar results.