The fermion dynamical symmetry model for the even--even and even--odd nuclei in the Xe--Ba region

摘要

The even--even and even--odd nuclei $^{126}$Xe-$^{132}$Xe and$^{131}$Ba-$^{137}$Ba are shown to have a well-realized $SO_8 \supset SO_6\supset SO_3$ fermion dynamical symmetry. Their low-lying energy levels can bedescribed by a unified analytical expression with two (three) adjustableparameters for even--odd (even--even) nuclei that is derived from the fermiondynamical symmetry model. Analytical expressions are given for wavefunctionsand for $E2$ transition rates that agree well with data. The distinctionbetween the FDSM and IBM $SO_6$ limits is discussed. The experimentallyobserved suppression of the the energy levels with increasing $SO_5$ quantumnumber $\tau$ can be explained as a perturbation of the pairing interaction onthe $SO_6$ symmetry, which leads to an $SO_5$ Pairing effect for $SO_6$ nuclei.