Multipole moments ofEr166,Er168,Yb174, andYb176from 65 MeV polarized proton inelastic scattering and density dependence of the effective interaction

Differential cross sections and analyzing powers of polarized proton elastic and inelastic scattering from ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$, and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$ have been measured at 65 MeV. Analysis for $J^{\pi }=0^{+}-6^{+}$ members of the ground state rotational band has been performed using coupled-channel calculations for scattering from deformed optical potentials. Excellent fits have been obtained for both cross sections and analyzing powers for $0^{+}$, $2^{+}$, and $4^{+}$ states and fairly good fits for the $6^{+}$ state. In the coupled-channel calculations, the multipole moments of each part of the deformed optical potentials were set to be equal. The quadrupole moments of the deformed optical potentials for these nuclei were found to be 4-6% larger than those of charge densities obtained by electron scattering and Coulomb excitation. A folding model calculation shows that the main part of this difference is attributed to the density dependence of the effective interaction. Mass number dependence of the phenomenological range of the effective interaction can be also reproduced from the folding calculation using the density-dependent effective interaction.