Coulomb excitation of ${}^{222}\mathrm{Rn}$

The nature of quadrupole and octupole collectivity in ${}^{222}\mathrm{Rn}$ was investigated by determining the electric-quadrupole ($E2$) and octupole ($E3$) matrix elements using subbarrier, multistep Coulomb excitation. The radioactive ${}^{222}\mathrm{Rn}$ beam, accelerated to 4.23 MeV/u, was provided by the HIE-ISOLDE facility at CERN. Data were collected in the Miniball $\gamma$-ray spectrometer following the bombardment of two targets, ${}^{120}\mathrm{Sn}$ and ${}^{60}\mathrm{Ni}$. Transition $E2$ matrix elements within the ground-state and octupole bands were measured up to $10\hslash$ and the results were consistent with a constant intrinsic electric-quadrupole moment, $518\left(11\right)e{\mathrm{fm}}^2$. The values of the intrinsic electric-octupole moment for the $0^{+}\to 3^{-}$ and $2^{+}\to 5^{-}$ transitions were found to be respectively ${2360}_{-210}^{+300}e{\mathrm{fm}}^3$ and ${2300}_{-500}^{+300}e{\mathrm{fm}}^3$ while a smaller value, ${1200}_{-900}^{+500}e{\mathrm{fm}}^3$, was found for the $2^{+}\to 1^{-}$ transition. In addition, four excited non-yrast states were identified in this work via $\gamma \text{−}\gamma$ coincidences.

Figure 1

Alpha-particle intensity detected in each front strip of one CD quadrant. The ordering of the strips presented start from the outermost strip to the innermost with increasing strip number. The solid red line corresponds to the best fit for $x$, the distance between the $\alpha$-particle source and the center of the detector, using Eq. (1). The dashed red lines correspond to a one-sigma uncertainty in $x$.

Figure 2

Particle energy versus scattering angle for the lower-energy ${}^{222}\mathrm{Rn}$ projectiles and higher-energy ${}^{120}\mathrm{Sn}$ recoils observed in the CD detector. The direction of the arrows correspond to an increasing scattering angle in the center-of-mass frame. The particle gate for recoiling target nuclei is shown as a solid black line.

Figure 3

Time difference between particle-$\gamma$ coincident events. The prompt coincidence window, highlighted in red, was 450 ns wide and the time-random coincidence window, highlighted in gray, was 600 ns wide.

Figure 4

Ratio of detector efficiency between the addback, reject, and segment modes with respect to the core mode. The data were collected using ${}^{152}\mathrm{Eu}$ and ${}^{133}\mathrm{Ba}$ calibration sources.

Figure 5

Spectra of $\gamma$ rays emitted following Coulomb excitation of ${}^{222}\mathrm{Rn}$ using a ${}^{120}\mathrm{Sn}$ target (blue) and a ${}^{60}\mathrm{Ni}$ target (red) observed in coincidence with recoiling target nuclei. The $\gamma$-ray energies were corrected for Doppler shift assuming they are emitted from the scattered projectile. Time-random coincidences between Miniball and CD detector have been subtracted. The spectra were obtained by sorting the data in the segment mode.

Figure 6

Background-subtracted $\gamma$-ray spectra observed in time-coincidence with other $\gamma$-ray transitions. The energy gate is labeled corresponding to the energies, spin, and parity of the initial and final states of the relevant transition. The transitions observed in coincidence with the gate are labeled with their energy given in keV. The spectra were obtained by sorting the data in the segment mode.

Figure 7

Level scheme of ${}^{222}\mathrm{Rn}$ showing all levels used in the gosia calculations. The levels in the positive-parity ground-state and negative-parity octupole bands were previously identified in Refs. [28, 29]. The non-yrast levels attributed to the $\gamma$ and $\beta$ bands were identified in this work from analysis of $\gamma \text{−}\gamma$ coincidences and are drawn with solid lines. The levels drawn with dashed lines were also included in the gosia fit, see text for details.

Figure 8

Calculated intensity of feeding from levels attributed to the $\beta$ band to the state $I^{\pi }$ relative to the total decay intensity of the state as a function of projectile energy for both the ${}^{120}\mathrm{Sn}$ (blue) and ${}^{60}\mathrm{Ni}$ (red) targets. In these experiments the range of projectile energies were 3.67–4.23 MeV/u for ${}^{120}\mathrm{Sn}$ and 3.49–4.23 MeV/u for ${}^{60}\mathrm{Ni}$.

Figure 9

Measured $\gamma$-ray intensities, divided by their respective scattering range in the center-of-mass (CoM) frame, for selected transitions in ${}^{222}\mathrm{Rn}$ collected with the ${}^{60}\mathrm{Ni}$ target. The dashed lines correspond to calculated intensities as a function of scattering angle $\theta$ in the CoM frame.

Figure 10

Values of intrinsic quadrupole moments $Q_2$ plotted as a function of spin (see Table 2). These values correspond to transitions between states with spin $I$ and $I-2$ with the exception of the diagonal matrix elements of the $2_1^{+}$ state. The value of the mean quadrupole moment, indicated by the red line, is obtained using the transitional matrix elements with the assumption that the ground-state and octupole bands have the same intrinsic moment.

Figure 11

The difference in aligned angular momentum, $\mathrm{\Delta }{i}_x=i_x^{-}-i_x^{+}$ plotted as a function of rotational frequency $\omega$. The upper dashed line corresponds to the vibrational limit $\mathrm{\Delta }{i}_x=3\hslash$. For the sources of the data, see Ref. [2] and references therein.

Figure 12

Calculated values of intrinsic octupole moments $Q_3$ taken from the adopted values in Table 2.

Figure 13

Measured intrinsic electric-octupole moments of Rn and Ra isotopes corresponding to the $\langle 0_1^{+}\left|\right|E3\left|\right|3_1^{-}\rangle$ reduced matrix elements. The experimental results, taken from this work and previous works [3, 4, 5], are compared with theoretical values using the 2-D Gogny D1S force (D1S) [36], QOCH with relativistic PC-PK1 EDF (RMF) [37] and covariant density EDF (CDFT) [38] for both Rn (red) and Ra (blue) isotopes and calculations using spdf-IBM-2 for Rn (red) isotopes (IBM) [39].