Surface diffuseness anomaly in heavy-ion potentials for large-angle quasielastic scattering

Recent high precision experimental data for heavy-ion fusion reactions at sub-barrier energies systematically show that a surprisingly large surface diffuseness parameter for a Woods-Saxon potential is required in order to fit the data. We point out that experimental data for quasielastic scattering at backward angles also favor a similar large value of the surface diffuseness parameter. Consequently, a double folding approach with a short-range imaginary potential for the compound nucleus formation fails to reproduce the experimental excitation function of quasielastic scattering for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ system at energies around the Coulomb barrier. We also show that the deviation of the ratio of the quasielastic to the Rutherford cross sections from unity at deep sub-barrier energies offers an unambiguous way to determine the value of the surface diffuseness parameter in the nucleus-nucleus potential.

Figure 1

The ratio of the quasielastic to the Rutherford cross sections at ${\theta }_{\mathrm{lab}}={170}^{°}$ (upper panel) and the fusion cross section (lower panel) for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ reaction. The solid line is obtained with the orientation-integrated formula with ${\beta }_2=0.306$ and ${\beta }_4=0.05$ by using the Woods-Saxon potential with the surface diffuseness parameter a of 1.05 fm; the dashed line is obtained with an a of 0.65 fm. The result of the double folding potential with the density-dependent M3Y interaction is denoted by the thin solid line. The experimental data are taken from Refs. 9, 15.

Figure 2

Effects of the deformation of the target nucleus on the quasielastic scattering for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ reaction. The meaning of the solid and dashed lines is the same as in Fig. 1. The dot-dashed and the dotted lines are obtained by assuming a spherical target for a Woods-Saxon potential with a surface diffuseness parameter a of 1.05 and 0.65 fm, respectively.