No-recoil approximation to the knock-on exchange potential in the double folding model for heavy-ion collisions

We propose the no-recoil approximation, which is valid for heavy systems, for a double folding nucleus-nucleus potential. With this approximation, the nonlocal knock-on exchange contribution becomes a local form. We discuss the applicability of this approximation for elastic scattering of the ${}^6\mathrm{Li}$ $+{}^{40}\mathrm{Ca}$ system. We find that, for this and heavier systems , the no-recoil approximation works as good as another widely used local approximation that employs a local plane wave for the relative motion between the colliding nuclei. We also compare the results of the no-recoil calculations with those of the zero-range approximation often used to handle the knock-on exchange effect.

Figure 1

The angular distribution of elastic ${}^6\mathrm{Li}$ $+{}^{40}\mathrm{Ca}$ scattering at $E_{\mathrm{lab}}=156.0$, 50.6, and 30.0 MeV obtained with several methods. The filled circles are the exact results of the integro-differential equation with the full nonlocal potential. The solid, dashed, and dotted lines are obtained in the no-recoil, local momentum, and zero-range approximations, respectively.