Multipole moments ofSm154andEr166by inelastic scattering of 134 MeV protons

Inelastic scattering of 134 MeV polarized protons from ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$ has yielded angular distributions of both cross sections and asymmetries for $J^{\pi }=0^{+} \mathrm{to} 6^{+}$ members of the ground state rotational bands. Deformation parameters ${\beta }_2$, ${\beta }_4$, and ${\beta }_6$ have been extracted from an analysis using coupled channels calculations for scattering from a deformed optical potential. The angular distributions of the cross sections have also been compared with an analytic eikonal model of the reaction. Multipole moments of the potential are determined and are compared with similar moments obtained from electromagnetic measurements and other hadron scattering experiments at different energies. A small energy dependence of the moments for ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ is observed. Comparisons are also made to moments obtained from Hartree-Fock calculations and from a liquid drop model. The observed hexadecapole moment of ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ is consistently higher than the theoretical predictions.