Quadrupole deformation of $^{130}$Xe measured in a Coulomb-excitation experiment

Low-lying states in the isotope $^{130}$Xe were populated in a Coulomb-excitation experiment performed at CERN's HIE-ISOLDE facility. The magnitudes and relative signs of seven $E2$ matrix elements and one $M1$ matrix element coupling five low-lying states in $^{130}$Xe were determined using the semiclassical coupled-channel Coulomb-excitation least-squares search code gosia. The diagonal $E2$ matrix elements of both the $2^+_1$ and $4^+_1$ states were extracted for the first time. The reduced transition strengths are in line with those obtained from previous measurements. Experimental results were compared with the general Bohr Hamiltonian with the microscopic input from mean-field theory utilizing universal nuclear energy density functional (UNEDF0), shell-model calculations using the GCN50:82 and SN100PN interactions, and simple phenomenological models (Davydov-Filippov and $γ$-soft). The extracted shape parameters indicate triaxial-prolate deformation in the ground-state band. In general, good agreement between theoretical predictions and experimental values was found, while neither phenomenological model was found to provide an adequate description of $^{130}$Xe.