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 $158\le A\le 170$. The values of the matrix elements $〈4^{+}\parallel M\left(E4\mathrm{}\right)\mathrm{}\parallel 0^{+}〉$ determined for ${\mathrm{Gd}}^{158,160}$, ${\mathrm{Dy}}^{162,164}$, and ${\mathrm{Er}}^{166,168,170}$ are 0.34 ± 0.11, 0.36 ± 0.10, 0.27 ± 0.10, 0.28 ± 0.11, ${0.06}_{-0.18\mathrm{}}^{+0.12\mathrm{}}$, ${0.20}_{-0.16\mathrm{}}^{+0.12\mathrm{}}$, and ${0.24}_{-0.18\mathrm{}}^{+0.14\mathrm{}}$, respectively. The $〈2^{+}\parallel M\left(E2\mathrm{}\right)\mathrm{}\parallel 0^{+}〉$ matrix elements were determined with a typical accuracy of about 1%. Model-dependent ${\beta }_2$ and ${\beta }_4$ deformation parameters are given.