Inelastic scattering exciting the $2^{+}$ and $4^{+}$ members of the $K^{\pi }$${=2\mathrm{}}^{+}$ γ-vibrational band in ${}_{}{}^{152}{}_{}{}^{}$,154Sm, ${}_{}{}^{160}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{166}{}_{}{}^{}$,168Er, ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{182}{}_{}{}^{}$,184W, and ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$ has been measured with 65-MeV polarized protons. Coupled-channel analyses have been performed assuming the γ-vibrational model or the asymmetric rotor model. A large hexadecapole ($Y_{42}$) term in the γ motion is necessary in both models in order to reproduce the experimental data. The quadrupole ($Y_{22}$) and hexadecapole ($Y_{42}$) transition strengths to the γ-vibrational band have been extracted systematically from the optical potential parameters and the deformation parameters for the first time. These show a strong mass number dependence, and can be understood qualitatively by a simple geometrical picture together with the quadrupole ($Y_{20}$) and hexadecapole ($Y_{40}$) moments. The experimental $Y_{22}$ and $Y_{42}$ strengths have been compared with a random-phase-approximation calculation. This suggests the importance of the hexadecapole degree of freedom in the γ vibration. A density-dependent Hartree-Fock calculation explains the quadrupole ($Y_{20}$) moments and the trend of the hexadecapole ($Y_{40}$) moments of the deformed optical potentials very well. The effect of the density dependence of the effective interaction is also discussed through the $Y_{20}$ moments and $Y_{22}$ strengths.

• Received 14 October 1986

DOI:https://doi.org/10.1103/PhysRevC.36.1754