Search for the $2^{+}_{3}$ to $0^{+}_{2}$ Transition in $^{158}$Gd

Interacting Boson Model 1 (IBM) calculations on Gadolinium nuclei indicate that the quadrupole deformation undergoes a phase transition. The IBM predicts that the deformation of the first excited $0^{+}_{2}$ state in $^{158}$Gd rises beyond that in $^{156}$Gd in a first order phase transition, while remaining smaller than that of the ground state [1]. This can be tested via measurement of quadrupole shape invariants. Coulomb excitation in conjunction with the YRAST-Ball array was used at the Yale ESTU tandem accelerator to excite the $2^+_3$ state in $^{158}$Gd and detect its transition of 63 keV to the $0^{+}_ {2}$ state. The intensity of this low-energy $\gamma$-ray has to be measured relative to decays around 900 keV. Therefore, an efficiency calibration with multiple sources covering the entire energy range was performed. \\ \noindent [1] V. Werner et al., Phys. Rev. C (R), submitted (2008).\\