Shell model study of $T=0$ states for ${}^{96}\mathrm{Cd}$ by the nucleon-pair approximation

In this paper we study the nucleon-pair approximation for $T=0$ states of ${}^{96}\mathrm{Cd}$ in the $1p_{1/2}1p_{3/2}0f_{5/2}0g_{9/2}$ shell with the JUN45 interaction. The lowest seniority scheme and the isoscalar spin-one pair approximation are not enough to describe the states. The isoscalar spin-aligned pair approximation is reasonably good for the yrast $2^{+}, 4^{+}, 6^{+}, {12}^{+}, {14}^{+}$, and ${16}^{+}$ states as pointed out previously. Not only the yrast positive-parity states but also nonyrast states and negative-parity states are well described by both the isovector pair approximation and the isoscalar pair approximation. We calculate overlaps between nucleon-pair basis states and shell-model wave functions. The largest overlaps and the corresponding nucleon-pair basis states are presented. We find that isovector spin-zero pairs, isovector spin-two pairs, and isoscalar spin-aligned pairs are the dominant building blocks in these states.

Figure 1

Yrast $T=0$ positive-parity states of ${}^{96}\mathrm{Cd}$ calculated in the $1p_{1/2}1p_{3/2}0f_{5/2}0g_{9/2}$ shell with JUN45 interaction. “SM” corresponds to the shell model, and “LS”, “SA”, “$J_{\max }$”, “SO”, “IV”, and “IS” correspond to the lowest seniority scheme, the spin-aligned pair approximation, the $J_{\max }$ pair approximation, the spin-one pair approximation, the isovector pair approximation, and the isoscalar pair approximation, respectively.

Figure 2

Overlaps between wave functions obtained in the $1p_{1/2}1p_{3/2}0f_{5/2}0g_{9/2}$ shell-model space and those obtained in nucleon-pair approximation subspaces, for the yrast $T=0$ positive-parity states of ${}^{96}\mathrm{Cd}$. “LS”, “SA”, “$J_{\max }$”, “SO”, “IV”, and “IS” are the same as in Fig. 1.

Figure 3

Electromagnetic properties for the yrast $T=0$ positive-parity states of ${}^{96}\mathrm{Cd}$ calculated in the $1p_{1/2}1p_{3/2}0f_{5/2}0g_{9/2}$ shell with JUN45 interaction: (a) reduced electric-quadrupole transition rates $B(E2;I⟶I-2)$, (b) electric-quadrupole moments $Q$, and (c) magnetic-dipole moments $\mu$. “SM”, “LS”, “SA”, “$J_{\max }$”, “SO”, “IV”, and “IS” are the same as in Fig. 1.

Figure 4

Same as Fig. 1 except for the yrast $T=0$ negative-parity states.

Figure 5

Same as Fig. 2 except for the yrast $T=0$ negative-parity states.

Figure 6

Electromagnetic properties for the yrast $T=0$ negative-parity states of ${}^{96}\mathrm{Cd}$: (a) reduced electric-quadrupole transition rates $B(E2;I⟶I-1)$, (b) reduced electric-quadrupole transition rates $B(E2;I⟶I-2)$, (c) electric-quadrupole moments $Q$, and (d) magnetic-dipole moments $\mu$. “SM”, “IV”, and “IS” are the same as in Fig. 1.