Structure of Xe126,128 studied in Coulomb excitation measurements

The electromagnetic properties of $^{126,128}\mathrm{Xe}$ were studied in subbarrier Coulomb excitation measurements performed at the National Superconducting Cyclotron Laboratory Re-accelerator facility, ReA3, at Michigan State University (MSU). $^{126}\mathrm{Xe}$ and $^{128}\mathrm{Xe}$ nuclei were accelerated to 3.74 and 3.81 MeV/nucleon, respectively, and were impinged on $^{196}\mathrm{Pt}$ and $^{208}\mathrm{Pb}$ targets. The $\ensuremath{\gamma}$ rays deexciting the populated low-lying states were detected in coincidence with the scattered nuclei using the JANUS setup. Transition and diagonal matrix elements for low-lying states and transitions in $^{126,128}\mathrm{Xe}$ were extracted from the experimental data using the gosia and gosia2 codes. The experimental results were compared with the theoretical calculations by the microscopic shell model and the Davydov-Filippov $\ensuremath{\gamma}$-rigid rotor model. The calculated results from the newly established shell model (called the PMMU model), which is based on the advanced Hartree-Fock Bogoliubov plus generator coordinate method (HFB $+$ gcm) for a large model space, agree well with the measurements in both nuclei, except for the second ${2}^{+}$ state. Interpretation for the experimentally determined nearly vanishing electric-quadrupole moment of this state remains a challenge for theory.