Figure 1

Evolution of the ratio $E(4_1^{+})/E(2_1^{+})$ as a function of the proton number in the isotone chains with $N=62,64,66,68,70,72$ (from left to right). The data are reported versus $A=N+Z$, to avoid overlapping of the different curves. A thicker line outlines data pertaining to the $N=66$ isotone chain. Horizontal lines show the theoretical values predicted by harmonic vibrator (V), X(5) model, and rigid rotator (R).Reuse & Permissions

Figure 2

Partial level scheme of ${}^{122}\mathrm{Ba}$ relevant for the present analysis. The two levels on the top of the band based on the $3_1^{+}$ state and the ${11}_1^{+}\to {10}_1^{+}$ transition have been identified in the present work.Reuse & Permissions

Figure 3

Evolution of the line shape of the $2_1^{+}\to 0_1^{+}$ of 196 keV (a), $4_1^{+}\to 2_1^{+}$ of 373 keV (b), and $6_1^{+}\to 4_1^{+}$ of 513 keV (c) $\gamma$ transitions at different target-to-stopper distances, in the experiment performed at LNL. These spectra have been taken at the most forward ring (${34.6}^{°}$ with respect to the beam), in coincidence with the Doppler-shifted part of the directly feeding transition. The size of the small 511-keV peak is visible in the lowest part of the right-hand panel.Reuse & Permissions

Figure 4

Gated $\gamma$-ray spectra of the $2_1^{+}$ $\to$ $0_1^{+}$ transition in the experiment performed in Cologne. On the left-hand side, the evolution with the distance of the shifted and unshifted peaks of the $2_1^{+}$ $\to$ $0_1^{+}$ transition registered by detectors positioned at an angle of ${29}^{°}$ with respect to the beam is shown. On the right-hand side is presented the same evolution registered by detectors positioned at a backward angle of ${143}^{°}$. The position of the unshifted (U) peak is indicated with a vertical line.Reuse & Permissions

Figure 5

Distribution of the stopping time of the ${}^{122}\mathrm{Ba}$ recoils according to the predictions of the Monte Carlo simulation for 10 000 histories. The velocity distribution at the entrance of the gold stopper is calculated for a ${}^{108}\mathrm{Cd}$ target thickness of 0.5 mg/cm${}^2$ (on a 2.3 mg/cm${}^2$ Ta facing the beam) and a beam energy of 69 MeV at the entrance of the target. The position of the mean value of the stopping time (814 fs) is indicated as a vertical arrow.Reuse & Permissions

Figure 6

Line-shape analysis of the $2_1^{+}\to 0_1^{+}$, 196-keV $\gamma$-ray transition and determination of the lifetime of the $J^{\pi }=2_1^{+}$ state, according to the procedure presented in [29]. On the left-hand side, spectra measured by the detectors of ring 1 (${34.6}^{°}$ with respect to the beam) in coincidence with a part of the shifted component of the $4_1^{+}\to 2_1^{+}$ transition, also taken on ring 1, and their fit (solid line) are shown at three distances. The fits of the unshifted peak and of the background are shown with the long-dashed line. The fitted DSA contribution (negligible in this case) is represented with a short-dashed line. The top panel on the right-hand side (rhs) shows the intensities of the unshifted component of the 196-keV transition, whereas the curve in the middle panel on the rhs corresponds to the derivative in the denominator of Eq. (1). The points reported in the bottom panel correspond to the mean life values deduced at the different distances. The value of $\tau$ corresponding to the best fit of results from ring 1 is shown by the central horizontal line and the uncertainty limits are drawn through the sensitivity region.Reuse & Permissions

Figure 7

Example of the line-shape analysis of the $4_1^{+}\to 2_1^{+}$, 373-keV transition and determination of the lifetime of the $J^{\pi }=4_1^{+}$ state. On the left-hand side, spectra in coincidence with a part of the shifted component of the $6_1^{+}\to 4_1^{+}$ transition, measured by the detectors of ring 7 (${145.4}^{°}$ with respect to the beam) and their fit (solid line) are shown at three distances. The meaning of the other panels is the same as in Fig. 6.Reuse & Permissions

Figure 8

Line-shape analysis of the $6_1^{+}\to 4_1^{+}$, 513-keV $\gamma$-ray transition measured at three different distances and registered by detectors from the forward ring 1 and determination of the lifetime of the $J^{\pi }=6_1^{+}$ state in ${}^{122}\mathrm{Ba}$. On the left-hand side the spectra obtained by setting a gate on the shifted component of the 620-keV transition, which feeds directly the level of interest, are shown. The meaning of the other panels is the same as in Fig. 6.Reuse & Permissions

Figure 9

Line-shape analysis of the $8_1^{+}\to 6_1^{+}$, 620-keV $\gamma$-ray transition measured at three different distances and registered by detectors from the forward ring 1 and determination of the lifetime of the $J^{\pi }=8_1^{+}$ state in ${}^{122}\mathrm{Ba}$. On the left-hand side the spectra obtained by setting a gate on the shifted component of the 694-keV transition, which feeds directly the level of interest, are shown. The importance of the DSA contribution (short-dashed line) is evident. The meaning of the other panels is the same as in Fig. 6.Reuse & Permissions

Figure 10

The ratio $R_{4/2}$ is shown as a function of $\zeta$ for the three indicated values of $\chi$ and $N_B=11$. The horizontal line shows the value predicted by the X(5) model; the vertical lines mark the values of $\zeta$ for which $R_{4/2}$ takes the value predicted by the X(5) model. In the inset, the Casten triangle is displayed.Reuse & Permissions

Figure 11

The experimental values (black solid circles) of the energy ratios (top part) and $B$($E$2) ratios (bottom part) of the g.s. band of ${}^{122}\mathrm{Ba}$ are compared with the X(5), U(5), and SU(3) predictions (solid lines), with the IBA-1 calculations (dashed lines [a], [b], and [c]) and with the IBA-2 calculations (open circles). The values of the parameters $\chi$ and $\zeta$ used in the IBA-1 calculations are given in the inset.Reuse & Permissions