Higher-Order Deformations ofTh232andU234,236,238

We have measured the inelastic scattering of 35-MeV protons from ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and from ${}_{}{}^{234,236,238}{}_{}{}^{}\mathrm{U}$. Angular distributions were extracted for $J^{\pi }=0^{+}-8^{+}$ members of the ground-state rotational bands, and were analyzed with use of coupled-channels calculations for scattering from a deformed optical potential. The deformation parameter ${\beta }_6$ is positive for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, nearly zero for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, and negative for ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The trends of the deformation parameters and multipole moments are explained qualitatively by a simple model.