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 $^{7}_Lambda$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 $^{25,27}_{Lambda}$Mg and $^{31}_{Lambda}$Si as examples, we analyse the impurity effects of $Lambda_s$ and $Lambda_p$ on the low-lying states of the core nuclei...
We discuss low-lying collective excitations of $Lambda$ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of $Lambda$ hypernuclei in the $sd$-shell region. Based on the relativistic mean-field (R
MF) approach, we show that the oblate deformation for $^{28}$Si nucleus may disappear when a $Lambda$ particle is added to this nucleus. We then discuss the rotational excitations of $^{25}_{Lambda}$Mg nucleus using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of $^{25}_{Lambda}$Mg nucleus is predicted to be slightly reduced due to an addition of $Lambda$ particle. We demonstrate that this leads to a reduction of electromagnetic transition probability, $B(E2)$, in the ground state rotational band. We also present an application of random phase approximation (RPA) to hypernuclei, and show that a new dipole mode, which we call a soft dipole $Lambda$ mode, appears in hypernuclei, which can be interpreted as an oscillation of $Lambda$ particle against the core nucleus.
The structure of low-energy collective states in proton-deficient N=28 isotones is analyzed using structure models based on the relativistic energy density functional DD-PC1. The relativistic Hartree-Bogoliubov model for triaxial nuclei is used to ca
lculate binding energy maps in the $beta$-$gamma$ plane. The evolution of neutron and proton single-particle levels with quadrupole deformation, and the occurrence of gaps around the Fermi surface, provide a simple microscopic interpretation of the onset of deformation and shape coexistence. Starting from self-consistent constrained energy surfaces calculated with the functional DD-PC1, a collective Hamiltonian for quadrupole vibrations and rotations is employed in the analysis of excitation spectra and transition rates of $^{46}$Ar, $^{44}$S, and $^{42}$Si. The results are compared to available data, and previous studies based either on the mean-field approach or large-scale shell-model calculations. The present study is particularly focused on $^{44}$S, for which data have recently been reported that indicate pronounced shape coexistence.
The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections {delta}c for the 0+to0+ superall
owed Fermi transitions. With these {delta}c values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% for all the employed relativistic energy functionals.
Quantum fluctuations concerning the shape of nuclei are treated within the framework of covariant density functional theory. Long range correlations beyond mean field are taken into account by configuration mixing of wave functions with triaxial shap
es and the restoration of spontaneously broken rotational symmetries through three-dimensional angular momentum projection. The controversial nucleus 16C is treated as an example and it is found that its ground state has a triaxial shape but with large shape fluctuations. They are of crucial importance for a proper description of the spectroscopic properties of such nuclei.
The ground-state properties of the recent reported proton emitter 145Tm have been studied within the axially or triaxially deformed relativistic mean field (RMF) approaches, in which the pairing correlation is taken into account by the BCS-method wit
h a constant pairing gap. It is found that triaxiality and pairing correlations play important roles in reproducing the experimental one proton separation energy. The single-particle level, the proton emission orbit, the deformation parameters beta = 0.22 and gamma = 28.98 and the corresponding spectroscopic factor for 145Tm in the triaxial RMF calculation are given as well.
