Low-energy extensions of the eikonal approximation to heavy-ion scattering

We discuss different schemes devised to extend the eikonal approximation to the regime of low bombarding energies (below 50 MeV per nucleon) in heavy-ion collisions. From one side we consider the first-and second-order corrections derived from Wallace's expansion. As an alternative approach we examine the procedure of accounting for the distortion of the eikonal straight-line trajectory by shifting the impact parameter to the corresponding classical turning point. The two methods are tested for different combinations of colliding systems and bombarding energies, by comparing the angular distributions they provide with the exact solution of the scattering problem. We find that the best results are obtained with the shifted trajectories, the Wallace expansion showing a slow convergence at low energies, in particular for heavy systems characterized by a strong Coulomb field.