Quadrupole and Hexadecapole Deformations in Rare-Earth Nuclei

Abstract

Electric quadrupole and hexadecapole transition matrix elements have been measured in precision Coulomb-excitation experiments with ${\mathrm{He}}^{4}$ particles for seven even-even targets in the mass range $158\ensuremath{\le}A\ensuremath{\le}170$. The values of the matrix elements $〈{4}^{+}\ensuremath{\parallel}M(E4)\ensuremath{\parallel}{0}^{+}〉$ determined for ${\mathrm{Gd}}^{158,160}$, ${\mathrm{Dy}}^{162,164}$, and ${\mathrm{Er}}^{166,168,170}$ are 0.34 \ifmmode\pm\else\textpm\fi{} 0.11, 0.36 \ifmmode\pm\else\textpm\fi{} 0.10, 0.27 \ifmmode\pm\else\textpm\fi{} 0.10, 0.28 \ifmmode\pm\else\textpm\fi{} 0.11, ${0.06}_{\ensuremath{-}0.18}^{+0.12}$, ${0.20}_{\ensuremath{-}0.16}^{+0.12}$, and ${0.24}_{\ensuremath{-}0.18}^{+0.14}$, respectively. The $〈{2}^{+}\ensuremath{\parallel}M(E2)\ensuremath{\parallel}{0}^{+}〉$ matrix elements were determined with a typical accuracy of about 1%. Model-dependent ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$ deformation parameters are given.