Deformation parameters of the charge distribution and the optical potential for some nuclei in and near the rare earth region

Abstract

Elastic and inelastic scattering of $\ensuremath{\alpha}$ particles on $^{154}\mathrm{Sm}$, $^{166}\mathrm{Er}$, $^{168}\mathrm{Er}$, $^{182}\mathrm{W}$, $^{184}\mathrm{W}$, and $^{186}\mathrm{W}$ was performed with incident energies between 11 and 21 MeV. Excitation functions for ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states of the ground-state rotational band were measured. Pronounced destructive nuclear-Coulomb interference effects were observed. Reduced $E2$ and $E4$ transition moments, and charge and optical-potential deformation parameters were determined from coupled-channel analysis of both the sub-Coulomb and interference data.NUCLEAR REACTIONS $^{154}\mathrm{Sm}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=11\ensuremath{-}19$ MeV; $^{166}\mathrm{Er}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=12.5\ensuremath{-}19.5$ MeV; $^{182}\mathrm{W}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=13\ensuremath{-}21$ MeV; measured $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}}, \ensuremath{\theta}=150\ifmmode^\circ\else\textdegree\fi{})$. $^{168}\mathrm{Er}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=13\ensuremath{-}19$ MeV; $^{184}\mathrm{W}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=12.5\ensuremath{-}19$ MeV; $^{186}\mathrm{W}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=13.25\ensuremath{-}19$ MeV, measured $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}}, \ensuremath{\theta}=140\ifmmode^\circ\else\textdegree\fi{}, 173.5\ifmmode^\circ\else\textdegree\fi{})$ deduced $\mathfrak{M}(E2)$, $\mathfrak{M}(E4)$, charge and optical potential deformations ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$; coupled channel calculation.