Understanding Xe isotopes near $A=130$ through the prolate-oblate shape phase transition

Abstract

A simple algebraic scheme incorporating the prolate-oblate shape phase transition (SPT) is proposed within the framework of the interacting boson model to describe the quadrupole deformation features of Xe isotopes near $A=130$. The analysis demonstrates that novel $γ$-soft modes, characterized by the unusual quadrupole moments $Q(2_1^+)<0$ and $0<Q(2_2^+)\ll |Q(2_1^+)|$, can emerge near the critical point of this SPT. This finding is further applied to interpret the properties of low-lying states in the relevant Xe nuclei, particularly the experimentally observed nearly vanishing spectroscopic quadrupole moment $Q(2_2^+)$, thereby offering new insights into the structure of a $γ$-soft deformed nucleus.

Figures (5)

• Figure 1: (a) The ground-state energy $E_\mathrm{g}$ evolves as a function of $k$, with the critical point $k_\mathrm{c}=3N/(2N+3)$ indicated by "Cri". (b) The same as in (a), but for the $\gamma$ deformations evaluated using Eq. (\ref{['gamma']}), where the green scatter points at the critical point represent the results for the degenerate SU(3) irreps $(\lambda,\mu)=(N-2t,t)$ with $t=2,~4,~6,~8$. (c) The same as in (b), but for the spectroscopic quadrupole moment $Q(2_1^+)$, where the $2_1^+$ state is assumed to originate from the $K=0$ band within a given $(\lambda,\mu)$. All results are obtained by solving the SU(3) Hamiltonian (\ref{['HSU3']}) for $N=10$.
• Figure 2: The contour plots for the classical potentials $V(\beta,\gamma)$, obtained at the critical point of the prolate-oblate SPT and in the O(6) limit (see the text for parameters), using the coherent-state method.
• Figure 3: (a) The evolutions of the $\gamma$ deformation, solved from the Hamiltonian (\ref{['H']}) as a function of $k$, is shown for $\eta=0.95$ and $\eta=0.85$, respectively. (b) The same as in (a), but for the $\gamma$ fluctuations. (c) The same as in (a), but for $Q(2_1^+)/e$ . (d) The same as in (a), but for $Q(2_2^+)/e$. (e) The same as in (a), but for the energy ratio $R_{4/2}$. The total boson number used in the calculations is fixed at $N=10$, and "Cri." denotes the critical point $k_\mathrm{c}=3N/(2N+3)$.
• Figure 4: The same as in Fig. \ref{['F3']}, but for $N=5$, with parallel dashed lines added to indicate where $Q(2_{1,2}^+)=0$.
• Figure 5: (A) The low-lying level pattern (normalized to $E(2_1^+)=1.0$) for $^{128}$Xe Elekes2015 and the corresponding critical point pattern ($N$=6), obtained from solving the Hamiltonian in (\ref{['H']}) with the parameter $\eta=0.88$ fixed to reproduce the experimental value of $R_{4/2}$. (B) The same as in (A), but for $^{130}$Xe Singh2001 and the critical point pattern ($N$=5), solved using $\eta=0.82$. (C) The same as in (A), but for $^{132}$Xe Khazov2005 and the critical point pattern ($N$=4), solved using $\eta=0.73$.