Systematic shell-model study of ${}^{99–129}\mathrm{Cd}$ isotopes and isomers in neutron-rich ${}^{127–131}\mathrm{In}$ isotopes

Systematic shell-model calculations are presented for odd-mass Cd isotopes with $N=51\text{−}81$ utilizing a combination of a $G$-matrix interaction and a semiempirical one. The excited energy spectra and electromagnetic transition probabilities are compared with the recently available experimental data. We have found that the observed quadrupole moments in the $11/2_1^{-}$ states that linearly change with the neutron number are well accounted for by the dominance of prolate shapes throughout the Cd isotope chain. We have also described the properties of several isomeric states in neutron-rich ${}^{127–131}\mathrm{In}$ isotopes that were recently observed in Jyväskylä.

Figure 1

Shell-model and experimental [25] energy levels of $2_1^{+}$ and $4_1^{+}$ states (top panel), and $B(E2:2_1^{+}\to 0_1^{+})$ values for even-mass ${}^{98–130}\mathrm{Cd}$ (bottom panel). The experimental data for $B\left(E2\right)$ values are taken from [26].

Figure 2

Comparison between calculated and experimental [25] energy levels for odd-mass ${}^{99–109}\mathrm{Cd}$.

Figure 3

Comparison between calculated and experimental [25] energy levels for odd-mass ${}^{111–121}\mathrm{Cd}$ isotopes.

Figure 4

Comparison between calculated and experimental [25] energy levels for odd-mass ${}^{123–129}\mathrm{Cd}$ isotopes. In the case of ${}^{125,127}\mathrm{Cd}$, we assume $X=186$ and 283.3 keV, respectively, and $X=0$ keV for ${}^{129}\mathrm{Cd}$ isotopes.

Figure 5

Comparison between calculated (left panel) and experimental (right panel) [25] energies of the $11/2^{-}$ band in odd-mass ${}^{103–129}\mathrm{Cd}$ isotopes.

Figure 6

Shell-model $B\left(E2\right)$ transition probabilities for even- and odd-mass Cd isotopes.

Figure 7

Comparison of shell-model results of $11/2^{-}$ band in odd-mass Cd isotopes with the ground state band in even-mass Cd isotopes.

Figure 8

Energy-surface plots for ${}^{111,119,125,129}\mathrm{Cd}$ isotopes. The red circles denote the energy minimum.

Figure 9

Comparison between calculated and experimental [44] $\mathrm{Q}(2_1^{+}$) for ${}^{98–130}\mathrm{Cd}$ isotopes.

Figure 10

Comparison between calculated and experimental [44] electric quadrupole (left) and magnetic dipole (right) moments of the $11/2_1^{-}$ state for odd-mass ${}^{105–129}\mathrm{Cd}$ isotopes.

Figure 11

Seniority of the $11/2_1^{-}$ states of Cd isotopes.

Figure 12

The $B\left(E2\right)$ ratios $R$ [see Eq. (3)] taken from the shell-model calculations (crosses) and those of fixed $K$ (dashed lines).

Figure 13

Comparison between calculated and experimental [25] energy levels for ${}^{127–131}\mathrm{In}$ isotopes.