Abstract

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, $^136Xe$ presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to $N=50$, the $\alpha$-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of $^100Sn$. 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 $^124Xe$. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null.Method: A stable $^124Xe$ beam with energies of $4.03A$ MeV and $4.11A$ MeV was used to bombard a $^natW$ 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 $VAMOS++$ magnetic spectrometer and the $\gamma$ 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 $^124Xe$. The present experimental data confirm that the O(6) symmetry is substantially broken in $^124Xe$.

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