Effect of long range potentials on the elastic cross section for theLi11+Pb208system

Abstract

For the $^{11}\mathrm{Li}+^{208}\mathrm{Pb}$ system, we find that the breakup process takes place from the forward angle or far distance region through the interaction distance which is obtained from ratios of elastic scattering cross sections to the Rutherford cross section. It is well known that the behavior of the $^{11}\mathrm{Li}+^{208}\mathrm{Pb}$ system is closely related to Coulomb dipole excitation effect. From the first ${\ensuremath{\chi}}^{2}$ analysis for the elastic cross section of the $^{9}\mathrm{Li}+^{208}\mathrm{Pb}$ system, we obtain the short-range potential of the $^{11}\mathrm{Li}+^{208}\mathrm{Pb}$ system by exploiting the optical model calculation for the Coulomb dipole excitation effect. To include the effect of the long-range interaction, we use a dynamic complex polarization potential including the Coulomb dipole potential and a long-range nuclear potential with Woods-Saxon form. Using the second ${\ensuremath{\chi}}^{2}$ analysis for the elastic cross section of the $^{11}\mathrm{Li}+^{208}\mathrm{Pb}$ system, we obtain the electric dipole transition probabilities $B(E1)$ which becomes 1.42 ${e}^{2}{\mathrm{fm}}^{2}$ and 1.41 ${e}^{2}{\mathrm{fm}}^{2}$ at ${E}_{\mathrm{c}.\mathrm{m}.}$ = 23.1 MeV and 28.3 MeV, respectively.