Using the REX-ISOLDE facility at CERN the Coulomb excitation cross sections for the $0_{\mathrm{gs}}^{+}\to 2_1^{+}$ transition in the $\beta$-unstable isotopes ${}^{100,102,104}\mathrm{Cd}$ have been measured for the first time. Two different targets were used, which allows for the first extraction of the static electric quadrupole moments $Q(2_1^{+})$ in ${}^{102,104}\mathrm{Cd}$. In addition to the $B(E2)$ values in ${}^{102,104}\mathrm{Cd}$, a first experimental limit for the $B(E2)$ value in ${}^{100}\mathrm{Cd}$ is presented. The data was analyzed using the maximum likelihood method. The provided probability distributions impose a test for theoretical predictions of the static and dynamic moments. The data are interpreted within the shell-model using realistic matrix elements obtained from a $G$-matrix renormalized CD-Bonn interaction. In view of recent results for the light Sn isotopes the data are discussed in the context of a renormalization of the neutron effective charge. This study is the first to use the reorientation effect for post-accelerated short-lived radioactive isotopes to simultaneously determine the $B(E2)$ and the $Q(2_1^{+})$ values.

• Received 20 May 2009

DOI:https://doi.org/10.1103/PhysRevC.80.054302