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

Background: The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the Λ 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 ArΛ37 and Ar36. 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 Λ binding energies in both ND and SD states of ArΛ37 are studied in the case of the Λ 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 Ar36 and ArΛs37 are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in ArΛ37 for all four effective interactions. Furthermore, the Λs reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For ArΛ37, the beyond-mean field decreases the Λs binding energy of the SD state by 0.17 MeV, but it almost has no effect on that of the ND state. Conclusions: In ArΛs37, the Λp and Λd binding energies of the SD states are always larger than those of the ND states. For Λs, the conclusion depends on the effective nucleon-hyperon interaction. Moreover, the beyond-mean-field model calculation indicates that the Λs hyperon is less bound in the SD state than that in the ND state.