A microscopic multiphonon approach is adopted to investigate the structure of some low-lying states observed experimentally in the $N=80$ isotones ${}^{134}\mathrm{Xe}$, ${}^{136}\mathrm{Ba}$, and ${}^{138}\mathrm{Ce}$. The calculation yields levels and electromagnetic transition strengths in good agreement with experiments and relates the observed selection rules to the neutron-proton symmetry and phonon content of the observed states. Moreover, it ascribes the splitting of the $M1$ strength in ${}^{138}\mathrm{Ce}$ to the proton subshell closure which magnifies the role of pairing in the excitation mechanism.

• Received 25 January 2008

DOI:https://doi.org/10.1103/PhysRevC.77.044310