Coulomb excitation of neutron-rich Cd isotopes

The isotopes ${}^{122,124,126}\mathrm{Cd}$ were studied in a “safe” Coulomb-excitation experiment at the radioactive ion-beam facility REX-ISOLDE at CERN. The reduced transition probabilities $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+}$) and limits for the quadrupole moments of the first 2${}^{+}$ excited states in the three isotopes were determined. The onset of collectivity in the vicinity of the $Z=50$ and $N=82$ shell closures is discussed by comparison with shell model and beyond mean-field calculations.

Figure 1

Miniball setup. (a) Target chamber for the Coulomb excitation setup, surrounded by the Ge cluster detectors. (b) Particle detector (DSSSD) and target wheel inside the target chamber.

Figure 2

Prompt $\gamma$-ray spectrum in coincidence with particles from the ${}^{122}\mathrm{Cd}$ measurement (no Doppler correction is applied). The (blue) solid line shows the spectrum taken in laser-on mode and the (red) dashed one in laser-off mode.

Figure 3

Total number of events in the Rutherford scattering peak in the particle detector as a function of 1/sin${}^4$(${\Theta }_{\mathrm{c}.\mathrm{m}.}/2$). Without an offset the angular ranges correspond to strips numbers 3, 4, 5, and 6 for each quadrant of the DSSSD detector. The lines are to guide the eye. The shape follows the Rutherford scattering cross section. (a) With the beam assumed to be passing through the geometric center of the DSSSD, (b) with the corrected beam position.

Figure 4

Particle-$\gamma$ time-difference spectrum. The windows of prompt and random coincidences are indicated.

Figure 5

Particle energy vs. scattering angle for the $A=124$ beam on a ${}^{64}\mathrm{Zn}$ target. The scattered projectiles can be clearly separated from the recoiling target nuclei.

Figure 6

Background-subtracted projectile Doppler-corrected $\gamma$-ray spectra taken in laser-on mode for the (a) ${}^{122}\mathrm{Cd}$, (b) ${}^{124}\mathrm{Cd}$, and (c) ${}^{126}\mathrm{Cd}$ measurement, respectively. The energies of the $2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ transitions in the projectile and target nuclei are indicated.

Figure 7

1$\sigma$ regions determined with the maximum-likelihood approach, for the diagonal $M_{22}$ and transition $M_{20}$ matrix elements for the $2_1^{+}$ state in (a) ${}^{122}\mathrm{Cd}$, (b) ${}^{124}\mathrm{Cd}$, and (c) ${}^{126}\mathrm{Cd}$. The error ellipses determine the possible combinations of $M_{22}$ and $M_{20}$ values for each isotope. For ${}^{126}\mathrm{Cd}$ two ellipses are shown—solid line contour, which includes only the Coulomb excitation data in the likelihood function and a density plot, created with a likelihood function which contains also the lifetime p.d.f. The solid lines in (a) and (c) represent the 1$\sigma$ boundary for $M_{20}$ derived from lifetime measurements.

Figure 8

${\chi }^2$ distribution for the DSAM fits (${\chi }_{\text{red,min}}^2=1.23$). At $\tau =9.9$ ps and $\tau =31.7$ ps the value of ${\chi }^2$ has changed by 1, which determines the standard deviation of the lifetime of the 2${}^{+}$ state (${\tau }_{2^{+}}=14.9$ ps).

Figure 9

Systematics of the $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to$2${}_1^{+}$) values for the cadmium isotopic chain as a function of the neutron number. The results from the shell-model calculation are marked with SM followed by the name of the interaction used in the calculation; Zamfir 1995 shows the results from Ref. [12].