Triaxially deformed relativistic point-coupling model for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>hypernuclei: A quantitative analysis of the hyperon impurity effect on nuclear collective properties

Abstract

Background: The impurity effect of hyperons 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 the hypernucleus ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Li}$. Many more data on low-lying states of $\ensuremath{\Lambda}$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $\ensuremath{\Lambda}$ impurity effect on nuclear low-energy excitations.Purpose: We carry out a quantitative analysis of the $\ensuremath{\Lambda}$ 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 $\ensuremath{\Lambda}$ hyperon is injected into the lowest positive-parity (${\ensuremath{\Lambda}}_{s}$) and negative-parity (${\ensuremath{\Lambda}}_{p}$) states.Method: We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $\ensuremath{\Lambda}$ binding energies of hypernuclei as well as the potential-energy surfaces (PESs) in the $(\ensuremath{\beta},\ensuremath{\gamma})$ deformation plane. We also calculate the PESs for the $\ensuremath{\Lambda}$ hypernuclei with good quantum numbers by 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 $_{\ensuremath{\Lambda}}^{25,27}\mathrm{Mg}$ and $_{\ensuremath{\Lambda}}^{31}\mathrm{Si}$ as examples, we analyze the impurity effects of ${\ensuremath{\Lambda}}_{s}$ and ${\ensuremath{\Lambda}}_{p}$ on the low-lying states of the core nuclei.Results: We show that ${\ensuremath{\Lambda}}_{s}$ increases the excitation energy of the ${2}_{1}^{+}$ state and decreases the $E2$ transition strength from this state to the ground state by $12%\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}17%$. On the other hand, ${\ensuremath{\Lambda}}_{p}$ tends to develop pronounced energy minima with larger deformation, although it modifies the collective parameters in such a way that the collectivity of the core nucleus can be either increased or decreased.Conclusions: The quadrupole deformation significantly affects the $\ensuremath{\Lambda}$ binding energies of deformed hypernuclei. A beyond-mean-field approach with the dynamical correlations due to restoration of broken symmetries and shape fluctuation is essential in order to study the $\ensuremath{\Lambda}$ impurity effect in a quantitative way.