Spectroscopic quadrupole moments in Xe124

Background: The Xe isotopic chain with four valence protons above the $Z=50$ shell closure is an ideal laboratory for the study of the evolution of nuclear deformation. At the $N=82$ shell closure, $^{136}\mathrm{Xe}$ presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to $N=50$, the $\ensuremath{\alpha}$-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of $^{100}\mathrm{Sn}$. Additionally, the Xe isotopes present higher order symmetries in the nuclear deformation such as the octupole degree of freedom near $N=60$ and $N=90$ or O(6) symmetry in stable isotopes.Purpose: The relevance of the O(6) symmetry has been investigated by measuring the spectroscopic quadrupole moment of the first excited states in $^{124}\mathrm{Xe}$. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null.Method: A stable $^{124}\mathrm{Xe}$ beam with energies of $4.03A$ MeV and $4.11A$ MeV was used to bombard a ${}^{\mathrm{nat}}\mathrm{W}$ target at the GANIL facility. Excited states were populated via the safe Coulomb excitation reaction. The collision of the heavy ions with a large $Z$ at low energy make this reaction sensitive to the diagonal $E2$ matrix element of the excited states. The recoils were detected in the $\mathrm{VAMOS}++$ magnetic spectrometer and the $\ensuremath{\gamma}$ rays in the AGATA tracking array. The least squares fitting code gosia was used for the analysis to extract both $E2$ and $M1$ transitional and $E2$ diagonal matrix elements.Results: The rotational ground state band was populated up to the ${8}_{1}^{+}$ state as well as the ${2}_{2}^{+}$ and ${4}_{2}^{+}$ states. Using high precision spectroscopic data to constrain the gosia fit, the spectroscopic quadrupole moments of the ${2}_{1}^{+}$, ${4}_{1}^{+}$, and ${6}_{1}^{+}$ states were determined for the first time.Conclusions: The spectroscopic quadrupole moments were found to be negative, large, and constant in the ground state band underlining the prolate axially deformed ground state band of $^{124}\mathrm{Xe}$. The present experimental data confirm that the O(6) symmetry is substantially broken in $^{124}\mathrm{Xe}$.