Description of the high spin states inGd146using the optimized Woods-Saxon potential

The Woods-Saxon potential is employed to interpret the properties of single particle and high spin spectra of ${}_{}{}^{146}{}_{}{}^{}\mathrm{Gd}$. Spin orbit potential parameters are found which simultaneously reproduce the experimental yrast and yrare states up to $I\sim 18$ and generate the proton single particle energy gap ${\delta }_p=2.0\mathrm{}$ MeV. The spin-orbit potential parameters obtained are nearly identical for neutrons and protons and are close to the parameter values obtained previously by optimizing the potential to high spin spectra in the vicinity of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Properties of the pairing correction method, the Bardeen-Cooper-Schrieffer approximation with blocking, and the particle number projection are discussed and illustrated. It is demonstrated that including the particle number projection term in the total energy formula improves considerably the average slope of the calculated yrast line. The possibility of the collective quadrupole vibrational states becoming yrast states is studied for $I\gtrsim 7\hslash$ using the random phase approximation but only a rather weak effect of collectivity is found in the spin-range studied.