Quadrupole and hexadecapole deformations in the actinide nuclei

Model-dependent deformation parameters, ${\beta }_{20}$ and ${\beta }_{40}$ are extracted from measured $E2\mathrm{}$ and $E4\mathrm{}$ transition moments for a distribution of nuclear charge represented by a three-parameter deformed Fermi distribution with a parabolic center depression. For the thorium and uranium nuclei this shape of the charge distribution reduces the extracted values of ${\beta }_{20}$ by 5-10% and ${\beta }_{40}$ by 10-15% from the values obtained with a two-parameter deformed Fermi distribution.