Excitation of the isovector giant dipole resonance by inelastic α scattering and the neutron skin of nuclei

Abstract

The cross section of the isovector giant dipole resonance (GDR) excited by inelastic scattering of 120-MeV \ensuremath{\alpha} particles for 0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\Theta}\ensuremath{\alpha}'\ensuremath{\le}3\ifmmode^\circ\else\textdegree\fi{} has been measured using the $^{116,124}\mathrm{Sn}$(\ensuremath{\alpha},\ensuremath{\alpha}'${\ensuremath{\gamma}}_{0}$) and $^{208}\mathrm{Pb}$(\ensuremath{\alpha},\ensuremath{\alpha}'${\ensuremath{\gamma}}_{0}$) reactions. The results are compared with distorted-wave Born-approximation calculations with a GDR form factor depending on the relative difference of proton and neutron radii (\ensuremath{\Delta}${\mathit{R}}_{\mathit{p}\mathit{n}}$/${\mathit{R}}_{0}$). Within the model used, the \ensuremath{\Delta}${\mathit{R}}_{\mathit{p}\mathit{n}}$/${\mathit{R}}_{0}$ values for $^{116}\mathrm{Sn}$, $^{124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ deduced from the comparison of measured and calculated cross sections are (0.${7}_{\mathrm{\ensuremath{-}}0.7}^{+2.3}$)%, (4.${1}_{\mathrm{\ensuremath{-}}2.5}^{+2.1}$)%, and (3.0\ifmmode\pm\else\textpm\fi{}1.3)%, respectively.