Structure of the doublet bands in doubly odd nuclei: The case of ${}^{128}\mathrm{Cs}$

The structure of the $\Delta J=1$ doublet bands in ${}^{128}\mathrm{Cs}$ is investigated within the framework of the interacting vector boson-fermion model. A new, purely collective interpretation of these bands is given on the basis of the used boson-fermion dynamical symmetry of the model. The energy levels of the doublet bands as well as the absolute $B(E2)$ and $B(M1)$ transition probabilities between the states of both yrast and yrare bands are described quite well. The observed odd-even staggering of both $B(M1)$ and $B(E2)$ values is reproduced by the introduction of an appropriate interaction term of quadrupole type, which produces such a staggering effect in the transition strengths. The calculations show that the appearance of doublet bands in certain odd-odd nuclei could be a consequence of the realization of a larger dynamical symmetry based on the noncompact supersymmetry group OSp(2$\Omega /12,\mathrm{R})$.

Figure 1

Comparison of the theoretical and experimental energies for the ground and $\gamma$ bands of ${}^{128}\mathrm{Xe}$. The values obtained for the model parameters entering in the core Hamiltonian (4) are $a=0.089\hspace{0.5em}09$, $b=-0.004\hspace{0.5em}59$, ${\alpha }_3=0.024\hspace{0.5em}71$, ${\beta }_3=0.031\hspace{0.5em}23$, and ${\alpha }_1=-0.019\hspace{0.5em}89$.

Figure 2

Comparison of the theoretical and experimental values for the $B(E2)$ transition probabilities between the states of the GSB in ${}^{128}\mathrm{Xe}$. The theoretical predictions of the rigid rotor and IBM are shown as well. The values of the model parameters are $e=1.46$ and $\theta =0.0014$.

Figure 3

Comparison of the theoretical and experimental energies for the lowest negative-parity states built on the $h_{11/2}$ configuration in ${}^{127}\mathrm{Xe}$.

Figure 4

Comparison of the theoretical and experimental energies for the lowest negative-parity states built on $h_{11/2}$ configuration in ${}^{129}\mathrm{Cs}$.

Figure 5

Comparison of the theoretical and experimental energies for the yrast and sidebands of ${}^{128}\mathrm{Cs}$. The theoretical predictions of the CQPCM are shown as well. The used values of the model parameters are as follows: $a=0.089\hspace{0.5em}09$, $b=-0.004\hspace{0.5em}59$, ${\alpha }_3=0.024\hspace{0.5em}71$, ${\beta }_3=0.031\hspace{0.5em}23$, ${\alpha }_1=-0.019\hspace{0.5em}89$, $\gamma =0.007\hspace{0.5em}38$, $\zeta =0.009\hspace{0.5em}86$, $\eta =0.113\hspace{0.5em}38,$ and $k=2.281\hspace{0.5em}15$.

Figure 6

Comparison of the theoretical and experimental values for the $B(E2)$ transition probabilities between the states of yrast and sidebands for ${}^{128}\mathrm{Cs}$. The theoretical predictions of the CQPCM and QCM are shown as well. The values of the model parameters are $e=0.86$ and $\theta =-0.0024$.

Figure 7

Theoretical values of the quadrupole moments $Q(J)$ as a function of the angular momentum J for both yrast and sidebands in ${}^{128}\mathrm{Cs}$.

Figure 8

Comparison of the theoretical and experimental values for the $B(M1)$ transition probabilities between the states of yrast and sidebands for ${}^{128}\mathrm{Cs}$. The theoretical predictions of the CQPCM and QCM are shown as well. The values of the model parameters are $g=0.58{\mu }_N$ and $g_{\mathrm{FG}}=-1.41{\mu }_N$.