Shapes of deformed nuclei as determined by electron scattering:Sm152,Sm154,Er166,Yb176,Th232, andU238

Electron scattering experiments have been performed on the deformed nuclei ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ at momentum transfers between 0.5 ${\mathrm{fm}}^{-1\mathrm{}}$ and 1.3 ${\mathrm{fm}}^{-1\mathrm{}}$. The cross sections for the $0^{+}$, $2^{+}$, and $4^{+}$ rotational states of these nuclei have been obtained and, together with other information on the electromagnetic properties of these nuclei, these data lead to information about the deformed shapes. The shapes of ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$ are quite different from the shapes of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ and require a varying skin thickness. The Sm isotopes require a constant skin thickness. Results are presented for ${\rho }_0\mathrm{}\left(r\right)\mathrm{}$, ${\rho }_2\mathrm{}\left(r\right)\mathrm{}$, and ${\rho }_4\mathrm{}\left(r\right)\mathrm{}$.