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...
The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $Napprox60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are
treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both $^{98}$Sr and $^{100}$Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for $^{98}$Sr and $^{100}$Zr. The resultant excitation energy of $0^+_2$ state and E0 transition strength $rho^2(E0;0^+_2rightarrow0^+_1)$ are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the $gamma$ deformation in $^{100}$Zr gives rise to the larger $rho^2(E0;0^+_2rightarrow0^+_1)$ than that in $^{98}$Sr.
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.
