Structure of even-even cadmium isotopes from the beyond-mean-field interacting boson model

The structure of even-even ${}^{108–116}\mathrm{Cd}$ isotopes is investigated based on the self-consistent mean-field approach. By mapping the quadrupole-$(\beta ,\gamma )$ deformation energy surface, obtained from the constrained self-consistent mean-field calculations with a choice of the Skyrme force and pairing property, onto the Hamiltonian of the interacting boson model with configuration mixing, the strength parameters of the Hamiltonian are determined. The low-lying excitation spectra and electric quadrupole and monopole transition rates for the considered Cd nuclei are computed by the resultant Hamiltonian, and are compared in detail with the experimental data. Our semimicroscopic prediction identifies several intruder states as suggested empirically, and overall, provides a reasonable qualitative description of the experimental energy levels and transition rates.

Figure 1

Left column: Contour plots for the $\beta \gamma$-deformation energy surfaces for ${}^{108–116}\mathrm{Cd}$, that have been obtained from the self-consistent mean-field (SCMF) calculation using the Skyrme SLy6 parametrization with the density-dependent zero-range pairing interaction with the strength $V_0=1000\mathrm{MeV}{\mathrm{fm}}^3$. Right column: the corresponding IBM-2 energy surfaces. Energy difference between neighboring contours is 250 keV. The global minimum is indicated by solid triangle, while the local minimum is identified by solid squares.

Figure 2

Same as Fig. 1, but for the calculation with the pairing strength of $V_0=1250\mathrm{MeV}{\mathrm{fm}}^3$ for the ${}^{112}\mathrm{Cd}$.

Figure 3

Experimental and predicted excitation spectra for ${}^{108–116}\mathrm{Cd}$.

Figure 4

Same as Fig. 3, but for the calculation on ${}^{112}\mathrm{Cd}$ based on the pairing strength increased by 25%.