Elastic and inelastic scattering measurements for theMg24+Pb208andSi28+Pb208systems

Abstract

The measurement and analysis of the differential cross sections for the elastic and inelastic scattering to the lowest ${2}^{+}$ states of $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$ using $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$ beams in conjunction with $^{208}\mathrm{Pb}$ targets are reported. The incident beam energies were 145 MeV for $^{24}\mathrm{Mg}$ and 162 MeV for $^{28}\mathrm{Si}$. The measured cross sections were analyzed using coupled channels calculations assuming a rotational model description for the low-lying collective states of $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$. The coupled channels calculations are compared with polarization potential calculations in which the experimental $B(E2)$ values are used in both cases. The extracted deformation lengths and deformation parameters are compared to those obtained using similar data with light projectiles, although because of strong Coulomb excitation the present calculations are fairly insensitive to the nuclear deformation parameters.NUCLEAR REACTIONS $^{208}\mathrm{Pb}$($^{24}\mathrm{Mg}$, $^{24}\mathrm{Mg}$), $^{208}\mathrm{Pb}$($^{24}\mathrm{Mg}$, $^{24}\mathrm{Mg}^{*}$) $Q=\ensuremath{-}1.37$ MeV, $E=145$ MeV; $^{208}\mathrm{Pb}$($^{28}\mathrm{Si}$, $^{28}\mathrm{Si}$), $^{208}\mathrm{Pb}$($^{28}\mathrm{Si}$, $^{28}\mathrm{Si}^{*}$) $Q=\ensuremath{-}1.78$ MeV, $E=162$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, ${\ensuremath{\theta}}_{\mathrm{lab}}=20\ensuremath{-}120\ifmmode^\circ\else\textdegree\fi{}$; optical model calculations including polarization potential, coupled channels calculations, extracted deformation parameters.