Deformation shrinking of the $\beta$-band at the first order shape phase transition

One main effect of the nuclear shape phase transition between spherical and deformed nuclei is the vast rise of the geometrical deformation parameter $\beta$ for the ground state towards deformed nuclei. This rise is reflected in a the rise of the model independent quadrupole shape invariant $q_2(0^+_1)$, from which an effecfive ground state $\beta$-deformation can be extracted. While one would naively expect similar behavior for the $q_2$ value of the first excited $0^+$ state, which corresponds to the head of the $\beta$-vibrational band, the IBM-1 predicts indeed a shrinking of its $\beta$-deformation when crossing the first order phase transition between vibrators and well-deformed nuclei. Absolute B(E2) values known for the ground-band and the $\beta$-band of $^{152,154}$Gd support this effect. This work is supported by USDOE under contract numbers DE-FG02-91ER-40609, and DFG under Br 799/12-1.