E2andE4Transition Moments and Equilibrium Deformations in the Actinide Nuclei

Abstract

Precision Coulomb-excitation experiments using ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions have been performed in the actinide region ($230\le A\le 248$) by the observation of elastic and inelastically scattered projectiles using a split-pole magnetic spectrometer equipped with a position-sensitive proportional detector. 12 even-$A$ targets from ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$ to ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}$ have been investigated and the reduced quadrupole matrix element, $〈2\parallel \mathfrak{M}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\parallel 0〉$, and the reduced hexadecapole matrix element, $〈4\parallel \mathfrak{M}\mathrm{}\left(E4\mathrm{}\right)\mathrm{}\parallel 0〉$, have been determined from the experimental excitation probabilities of the $0^{+}$, $2^{+}$, and $4^{+}$ states in the ground-state rotational bands. The values of $B(E4,0\mathrm{}\to 4)$ range from 167 single-particle units for ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ to essentially zero single-particle units for ${}_{}{}^{244,246,248}{}_{}{}^{}\mathrm{Cm}$. Model-dependent deformation parameters, ${\beta }_{20}$ and ${\beta }_{40}$, are extracted from the measured $E2\mathrm{}$ and $E4\mathrm{}$ transition moments for distributions of nuclear charge represented by deformed Fermi distributions and by a deformed homogeneous distribution.