Low-lying collectively excited states of ${}^{128}\mathrm{Xe}$ were investigated by $\gamma$-ray spectroscopy following the ${}^{12}\mathrm{C}({}^{128}\mathrm{Xe},{}^{128}\mathrm{Xe}{}^{*}){}^{12}\mathrm{C}$ projectile Coulomb excitation reaction. Nineteen absolute $E2$ transition strengths were obtained including the first measurement of the critical $B(E2)$ decays from the second and third $J^{\pi }=0^{+}$ states. These data are compared with the theoretical predictions of the critical point symmetry E(5) and allow us to conclude that ${}^{128}\mathrm{Xe}$ is not an E(5) nucleus as previously suggested, leaving ${}^{130}\mathrm{Xe}$ as the most likely candidate among the Xe isotopes.

• Received 16 November 2009

DOI:https://doi.org/10.1103/PhysRevC.80.061304