Triaxially deformed relativistic point-coupling model for $Λ$ hypernuclei: a quantitative analysis of hyperon impurity effect on nuclear collective properties

The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Λ$Li. Many more data on low-lying states of $Λ$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Λ$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Λ$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $Λ$ hyperon is injected into the lowest positive-parity ($Λ_s$) and negative-parity ($Λ_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $Λ$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(β, γ)$ deformation plane. We also calculate the PESs for the $Λ$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_Λ$Mg and $^{31}_Λ$Si as examples, we analyse the impurity effects of $Λ_s$ and $Λ_p$ on the low-lying states of the core nuclei...