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

摘要

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 _Λ~(37) Ar and ~(36)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 Λ binding energies in both ND and SD states of _Λ~(37) Ar 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 ~(36)Ar and _Λ~(37)_sAr are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in _Λ~(37) Ar for all four effective interactions. Furthermore, the Λ_s reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For _Λ~(37) Ar, the beyond-mean field decreases the Λ_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 _Λ_s~(37) Ar, the Λ_p and Λ_d binding energies of the SD states are always larger than those of the ND states. For Λ_s , the conclusion depends on the effective nucleon-hyperon interaction. Moreover, the beyond-mean-field model calculation indicates that the Λ_s hyperon is less bound in the SD state than that in the ND state.