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 $\ensuremath{\alpha}$ particles at energies below those where nuclear effects are expected to contribute significantly. Charge deformation parameters ${\ensuremath{\beta}}_{2}^{c}$ and ${\ensuremath{\beta}}_{4}^{c}$ 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 $〈{0}^{+}\ensuremath{\parallel}(E2)\ensuremath{\parallel}{2}^{+}〉$ 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 \ensuremath{\lesssim}1% uncertainty. The values of $〈{0}^{+}\ensuremath{\parallel}M(E4)\ensuremath{\parallel}{4}^{+}〉$ for these same respective nuclei are ${0.21}_{\ensuremath{-}0.20}^{+0.16}$, ${0.16}_{\ensuremath{-}0.15}^{+0.10}$, ${0.16}_{\ensuremath{-}0.26}^{+0.14}$, ${0.12}_{\ensuremath{-}0.13}^{+0.12}$, and ${0.19}_{\ensuremath{-}0.19}^{+0.14}$ ${\mathit{e}\mathrm{b}}^{2}$.NUCLEAR REACTIONS $^{156,159}\mathrm{Dy}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{162,164}\mathrm{Er}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, $^{168}\mathrm{Yb}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=12\ensuremath{-}13$ MeV; measured Coulomb excitation cross sections relative to elastic cross sections at ${\ensuremath{\theta}}_{\mathrm{lab}}=150\ifmmode^\circ\else\textdegree\fi{}$; deduced $〈{0}^{+}\ensuremath{\parallel}M(E2)\ensuremath{\parallel}{2}^{+}〉$, $〈{0}^{+}\ensuremath{\parallel}M(E4)\ensuremath{\parallel}{4}^{+}〉$, using rotational model; extracted charges deformation parameters ${\ensuremath{\beta}}_{2}^{c}$, ${\ensuremath{\beta}}_{4}^{c}$ from rotational model and Fermi charge distribution. Enriched targets.