Coulomb excitation measurements of reducedE2andE4transition matrix elements inDy156,158,Er162,164, andYb168

Abstract

The reduced $E2$ and $E4$ transition matrix elements were measured for ${}_{}{}^{156,158}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{162,164}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$ via Coulomb excitation with $\alpha$ particles at energies below those where nuclear effects are expected to contribute significantly. Charge deformation parameters ${\beta }_2^c$ and ${\beta }_4^c$ were extracted from these matrix elements by assuming the charge distribution to have a deformed Fermi distribution form with quadrupole and hexadecapole components. Values of $〈0^{+}\parallel \left(E2\right)\parallel 2^{+}〉$ of 1.929, 2.161, 2.238, 2.341, and 2.402 eb were found for ${}_{}{}^{156,158}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{162,164}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$, respectively, with ≲1% uncertainty. The values of $〈0^{+}\parallel M\left(E4\right)\parallel 4^{+}〉$ for these same respective nuclei are ${0.21}_{-0.20\mathrm{}}^{+0.16\mathrm{}}$, ${0.16}_{-0.15\mathrm{}}^{+0.10\mathrm{}}$, ${0.16}_{-0.26\mathrm{}}^{+0.14\mathrm{}}$, ${0.12}_{-0.13\mathrm{}}^{+0.12\mathrm{}}$, and ${0.19}_{-0.19\mathrm{}}^{+0.14\mathrm{}}$ ${\mathit{e}\mathrm{b}}^2$.