Nuclear charge radii and shape evolution of Kr and Sr isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is employed to study the ground-state properties of Kr and Sr isotopes. Based on the constrained DRHBc calculations, it is found that Kr and Sr isotopes with $N=50$ are spherical, while the nuclei just away from $N=50$ generally have soft potential energy curves. Further moving along the isotopic chains in both neutron-rich and neutron-deficient directions, there are generally two minima at oblate and prolate sides for nuclear potential energy curves, where possible candidates for shape coexistence are found. The dynamical correlations are crucial to describe the properties of nuclei with soft potential energy curves or shape coexistence, e.g., the binding energies, two-neutron separation energies, deformations, and charge radii, which are considered with the two-dimensional collective Hamiltonian method. In addition, the constrained DRHBc calculations would be helpful to distinguish the oblate or prolate shape for the nuclei with deformation $|{\beta }_2|\gtrsim 0.3$ by combining with the experimental charge radii and absolute values of deformations.

Figure 1

Differences between the experimental binding energies [121] and the theoretical results for Kr (a) and Sr (b) isotopes. The DRHBc results, DRHBc results with $E_{\mathrm{rot}}$, and $\mathrm{DRHBc}+\mathrm{2DCH}$ results are shown by open squares, triangles, and circles, respectively.

Figure 2

Comparison of $S_{2n}$ between experimental data [121] (filled squares) and theoretical results for Kr (a) and Sr (b) isotopes. The DRHBc results, DRHBc results with $E_{\mathrm{rot}}$, and $\mathrm{DRHBc}+\mathrm{2DCH}$ results are shown by open squares, triangles, and circles, respectively.

Figure 3

Evolution of the PECs for Kr (a) and Sr (b) isotopes from the constrained DRHBc calculations. For displaying the data clearly, the PECs of the lightest isotopes ${}^{70}\mathrm{Kr}$ and ${}^{76}\mathrm{Sr}$ are renormalized to their potential energies at ${\beta }_2=0$, and other PECs for each isotope are shifted upward by 4 MeV compared to the previous one.

Figure 4

Charge radii and deformations for Kr and Sr isotopes. The results from the $\mathrm{DRHBc}+\mathrm{2DCH}$ and DRHBc calculations are denoted with open circles and open squares, respectively. The green triangles (c) and (d) represent the new $\mathrm{DRHBc}+\mathrm{2DCH}$ calculations, while the pairing strength is reduced by multiplying a factor of 0.8. The corresponding experimental data [17, 122] are shown with filled squares for comparison.

Figure 5

Charge radius as a function of deformation for ${}^{100}\mathrm{Sr}$. The filled and open circles denote the constrained results and the minima in unconstrained calculations predicted by the DRHBc model. The dependence between the charge radius and the deformation from a empirical formula [124] is shown with the squares for comparison. Shadows represent experimental charge radius [17] and deformation [122] with uncertainties.

Figure 6

Wave function of ${}^{100}\mathrm{Sr}$ in the 2DCH model.

Figure 7

Charge radii from the constrained DRHBc calculations for Kr (a) and Sr (b) isotopes. The deformations in DRHBc calculations are constrained to the experimental values [122] in the prolate (open inverted triangles) and oblate (open triangles) regions. The experimental charge radii [17] are shown with filled squares for comparison.