The even-even and even-odd nuclei ${}_{}{}^{126}{}_{}{}^{}–_{}^{132}{}_{}{}^{}$Xe and ${}_{}{}^{131}{}_{}{}^{}–_{}^{137}{}_{}{}^{}$Ba are shown to have a well-realized ${\mathrm{SO}}_8$⊃${\mathrm{SO}}_6$⊃${\mathrm{SO}}_3$ fermion dynamical symmetry. Their low-lying energy levels can be described by a unified analytical expression with two (three) adjustable parameters for even-odd (even-even) nuclei that is derived by using the vector and spinor representations of the fermion model. Analytical expressions are given for wave functions and for E2 transition rates that agree well with data. The distinction between the fermion dynamical symmetry model (FDSM) and the interacting boson model (IBM) ${\mathrm{SO}}_6$ limits is discussed. The experimentally observed suppression of the energy levels with increasing ${\mathrm{SO}}_5$ quantum number τ can be explained as a perturbation of the pairing interaction on the ${\mathrm{SO}}_6$ symmetry, which leads to an ${\mathrm{SO}}_5$ pairing effect for ${\mathrm{SO}}_6$ nuclei. © 1996 The American Physical Society.

• Received 27 July 1995

DOI:https://doi.org/10.1103/PhysRevC.53.715