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The impurity effect of hyperon on atomic nuclei has received a renewedinterest in nuclear physics since the first experimental observation ofappreciable reduction of $E2$ transition strength in low-lying states ofhypernucleus $^{7}_\Lambda$Li. Many more data on low-lying states of $\Lambda$hypernuclei will be measured soon for $sd$-shell nuclei, providing goodopportunities to study the $\Lambda$ impurity effect on nuclear low-energyexcitations. We carry out a quantitative analysis of $\Lambda$ hyperon impurityeffect on the low-lying states of $sd$-shell nuclei at the beyond-mean-fieldlevel based on a relativistic point-coupling energy density functional (EDF),considering that the $\Lambda$ hyperon is injected into the lowestpositive-parity ($\Lambda_s$) and negative-parity ($\Lambda_p$) states. Weadopt a triaxially deformed relativistic mean-field (RMF) approach forhypernuclei and calculate the $\Lambda$ binding energies of hypernuclei as wellas the potential energy surfaces (PESs) in $(\beta, \gamma)$ deformation plane.We also calculate the PESs for the $\Lambda$ hypernuclei with good quantumnumbers using a microscopic particle rotor model (PRM) with the samerelativistic EDF. The triaxially deformed RMF approach is further applied inorder to determine the parameters of a five-dimensional collective Hamiltonian(5DCH) for the collective excitations of triaxially deformed core nuclei.Taking $^{25,27}_{\Lambda}$Mg and $^{31}_{\Lambda}$Si as examples, we analysethe impurity effects of $\Lambda_s$ and $\Lambda_p$ on the low-lying states ofthe core nuclei...

physical review. c. nuclear physics/physical review. c, nuclear physics

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