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

Abstract

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 ${}_{\Lambda }^7$Li. Many more data on low-lying states of $\Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $\Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $\Lambda$ 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 $\Lambda$ hyperon is injected into the lowest positive-parity (${\Lambda }_s$) and negative-parity (${\Lambda }_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $\Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(\beta ,\gamma )$ deformation plane. We also calculate the PESs for the $\Lambda$ 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 ${}_{\Lambda }^{25,27}$Mg and ${}_{\Lambda }^{31}$Si as examples, we analyse the impurity effects of ${\Lambda }_s$ and ${\Lambda }_p$ on the low-lying states of the core nuclei...

15 pages with 18 figures and 1 table (version to be published in Physical Review C)

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