Beyond-mean-field study of the hyperon impurity effect in hypernuclei with shape coexistence

Abstract

Background: The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the $\mathrm{\ensuremath{\Lambda}}$ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states.Purpose: This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy.Method: The models of relativistic mean field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying states of both $_{\mathrm{\ensuremath{\Lambda}}}^{37}\mathrm{Ar}$ and $^{36}\mathrm{Ar}$. The wave functions of low-lying states are constructed as a superposition of a set of relativistic mean-field states with different values of quadrupole deformation parameter. The projections onto both particle number and angular momentum are considered.Results: The $\mathrm{\ensuremath{\Lambda}}$ binding energies in both ND and SD states of $_{\mathrm{\ensuremath{\Lambda}}}^{37}\mathrm{Ar}$ are studied in the case of the $\mathrm{\ensuremath{\Lambda}}$ hyperon occupying the $s,p$, or $d$ state in the spherical limit, respectively. For comparison, four sets of nucleon-hyperon point-coupling interactions are used, respectively. Moreover, the spectra of low-lying states in $^{36}\mathrm{Ar}$ and $_{{\mathrm{\ensuremath{\Lambda}}}_{s}}^{37}\mathrm{Ar}$ are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in $_{\mathrm{\ensuremath{\Lambda}}}^{37}\mathrm{Ar}$ for all four effective interactions. Furthermore, the ${\mathrm{\ensuremath{\Lambda}}}_{s}$ reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For $_{\mathrm{\ensuremath{\Lambda}}}^{37}\mathrm{Ar}$, the beyond-mean field decreases the ${\mathrm{\ensuremath{\Lambda}}}_{s}$ binding energy of the SD state by 0.17 MeV, but it almost has no effect on that of the ND state.Conclusions: In $_{{\mathrm{\ensuremath{\Lambda}}}_{s}}^{37}\mathrm{Ar}$, the ${\mathrm{\ensuremath{\Lambda}}}_{p}$ and ${\mathrm{\ensuremath{\Lambda}}}_{d}$ binding energies of the SD states are always larger than those of the ND states. For ${\mathrm{\ensuremath{\Lambda}}}_{s}$, the conclusion depends on the effective nucleon-hyperon interaction. Moreover, the beyond-mean-field model calculation indicates that the ${\mathrm{\ensuremath{\Lambda}}}_{s}$ hyperon is less bound in the SD state than that in the ND state.