Systematic investigations of the stable Cd isotopes

The Cd nuclei, especially the stable even-even isotopes have been well studied since they were suggested as paradigms of the vibrational, or $U(5)$, limit of the Interacting Boson Model (IBM). In addition to the normal quadrupole phonon states, in many cases suggested up to the three-phonon quintuplet, more deformed $2p4h$ intruder excitations have been established. Recent investigations with the $(n,n^{\prime}\gamma)$ reaction [1,2,3,4] have provided a wealth of information on the low-lying levels, including many lifetimes not previously known. Deviations in the transition $B(E2)$ values for low-spin states from those expected for $U(5)$ nuclei are observed to appear systematically across the Cd isotopes. We have performed detailed calculations using the IBM-2, and find that these deviations cannot be explained through considered mixings with the intruder excitations or mixed-symmetry states, indicating that some physics is missing in the description of these levels. \break \noindent [1] F. Corminboeuf {\it et al.}, Phys. Rev. C {\bf 63}, 014305 (2001).\hfill \break \noindent [2] P.E. Garrett {\it et al.}, Phys. Rev. C {\bf 75}, 014307 (2007).\hfill\break \noindent [3] D. Bandyopadhyay {\it et al.}, {\it to be published}. \hfill\break \noindent [4] M. Kadi {\it et al.}, Phys. Rev. {\bf 68}, 031306 (2003). \hfill