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

Abstract

The even--even and even--odd nuclei ${}^{126}$Xe-${}^{132}$Xe and ${}^{131}$Ba-${}^{137}$Ba are shown to have a well-realized $S{O}_8\supset S{O}_6\supset S{O}_3$ 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 from the fermion dynamical symmetry model. Analytical expressions are given for wavefunctions and for $E2$ transition rates that agree well with data. The distinction between the FDSM and IBM $S{O}_6$ limits is discussed. The experimentally observed suppression of the the energy levels with increasing $S{O}_5$ quantum number $\tau$ can be explained as a perturbation of the pairing interaction on the $S{O}_6$ symmetry, which leads to an $S{O}_5$ Pairing effect for $S{O}_6$ nuclei.

Comments: submitted to Phys. Rev. C, LaTeX, 31 pages, 8 figures with postscript files available on request at pan@einstein.physics.drexel.edu