Spectroscopic quadrupole moments in ${}^{124}\mathrm{Xe}$

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 $\alpha$-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 $\gamma$ 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 ${}^{124}\mathrm{Xe}$.

Figure 1

Kinematic lines (scattering angle as a function of the velocity) measured at the entrance of $\mathrm{VAMOS}++$. Continuous red (blue) shows the Xe beam scattered at maximum (minimum) energy on W detected in $\mathrm{VAMOS}++$; dashed red (blue) shows the W target scattered by the Xe beam at maximum (minimum) energy detected in $\mathrm{VAMOS}++$. Green is the kinematic line for the Xe beam scattered on the carbon backing, excluded by the detection system; black shows Xe beam scattered on the iron target.

Figure 2

Prompt $\gamma$-ray spectrum following the de-excitation of ${}^{182,184,186}\mathrm{W}$ after Coulomb excitation measured in AGATA.

Figure 3

Prompt $\gamma$-ray spectrum following the de-excitation of ${}^{124}\mathrm{Xe}$ after safe Coulomb excitation at the beam energy of $4.03A$ MeV.

Figure 4

Partial level scheme of ${}^{124}\mathrm{Xe}$ with observed transitions. Additional states included in the analysis are also shown.

Figure 5

${\chi }^2$ scans for the $E2$ the $3^{+}\to 2_2^{+}$ (full circles) and $4_2^{+}\to 4_1^{+}$ (open circles) ($e\mathrm{b}$) and $M1$ $4_2^{+}\to 4_1^{+}$ (red triangle) (${\mu }_N$) matrix elements.

Figure 6

${\chi }^2$ scan on the $2_1^{+}$ diagonal matrix element. Only this matrix element was permitted to vary, others remain fixed.

Figure 7

Stability of the solution under different assumptions. In red, ${}^{\mathrm{nat}}\mathrm{W}$ is considered as mixed in Fe, i.e., cross sections are integrated over the full Fe thickness. In blue, the W is facing VAMOS, i.e., cross sections are calculated at the lowest beam energy (Table 3). The light (dark) gray assumes a misalignment in scattering angle of $\pm 3$ degrees in the laboratory frame, respectively. In violet, the minimization is forced to low $Q_s$ and constrained released for final solution. In green, all lifetimes are a free parameter of the minimization.

Figure 8

Top: Spectroscopic quadrupole moment systematics as a function of the neutron number for Sn, Te, Xe, and Ba elements. The present work is highlighted in blue for ${}^{124}\mathrm{Xe}$. The recent measurements in ${}^{126\text{–}130}\mathrm{Xe}$ [10, 33] are shown in red. Bottom: Reduced transition probability systematics as a function of the neutron number for Sn, Te, Xe, and Ba elements.