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

Low-lying states in the isotope ${}^{130}\mathrm{Xe}$ 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 ${}^{130}\mathrm{Xe}$ 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 $\gamma$-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 ${}^{130}\mathrm{Xe}$.

Figure 1

The particle spectrum collected in the DSSSD detector, displaying the projectile and target kinematics for the Coulomb excitation of ${}^{130}\mathrm{Xe}$ on a ${}^{94}\mathrm{Mo}$ target. The red outline indicates the region gated on for target-like events.

Figure 2

A particle-$\gamma$ coincidence plot showing the time-gating conditions used in the experiment. The peak displays events fulfilling the particle-$\gamma$ coincidence condition. The selected prompt window was 450 ns wide (shown in gray), and the random window was set to 600 ns (shown in red).

Figure 3

The particle-particle-$\gamma$ coincidence spectrum collected in the Coulomb excitation of a ${}^{130}\mathrm{Xe}$ beam on a ${}^{94}\mathrm{Mo}$ target experiment, gated on the recoil-like particles, Doppler corrected for the ${}^{130}\mathrm{Xe}$ projectile velocity. All observed transitions in the Coulomb-excited ${}^{130}\mathrm{Xe}$ are labeled. The energy region in the spectrum between 800 and 950 keV corresponds to the Doppler-broadened $2_1^{+}$ $\to$ $0_1^{+}$ transition at 871 keV in the ${}^{94}\mathrm{Mo}$ target.

Figure 4

Low-lying excited states in ${}^{130}\mathrm{Xe}$, considered in the present analysis. Transitions observed in the current experiment with a ${}^{94}\mathrm{Mo}$ target are marked in red. Level and transition energies are given in keV.

Figure 5

Potential energy surface map (relative to a spherical shape value) for the ground state of ${}^{130}\mathrm{Xe}$, computed using the GBH-UNEDF0 functional. A pronounced $\gamma$-soft shape is visible for $\beta$ ranging from 0 up to 0.3.

Figure 6

Experimental [3] and theoretical low-lying energy level schemes for ${}^{130}\mathrm{Xe}$. See the text for the details of the calculations.

Figure 7

The diagonal matrix element $\langle 2_1^{+}\left|\right|E2\left|\right|2_1{}^{+}\rangle$ in ${}^{130}\mathrm{Xe}$, normalized to the $\langle 2_1^{+}\left|\right|E2\left|\right|0_1{}^{+}\rangle$ transitional matrix element, as a function of the $\gamma$ deformation parameter [60]. The solid black line represents the results of the Davydov-Filippov model, the yellow shaded area corresponds to the values of matrix elements determined in the present study (with $1\sigma$ uncertainty), and the blue shaded area shows the result of the quadrupole sum rules analysis for the ${}^{130}\mathrm{Xe}$ ground state.

Figure 8

Plot of the potential energy function (1), used in the phenomenological $\gamma$-soft collective model.