LOW-ENERGY EXTENSIONS OF THE EIKONAL APPROXIMATION TO HEAVY-ION SCATTERING

We discuss different schemes devised to extend the eikonal approximati on to the regime of low bombarding energies (below 50 MeV per nucleon) in heavy-ion collisions. From one side we consider the first-and seco nd-order corrections derived from Wallace's expansion. As an alternati ve approach we examine the procedure of accounting for the distortion of the eikonal straight-line trajectory by shifting the impact paramet er to the corresponding classical turning point. The two methods are t ested for different combinations of colliding systems and bombarding e nergies, by comparing the angular distributions they provide with the exact solution of the scattering problem. We find that the best result s are obtained with the shifted trajectories, the Wallace expansion sh owing a slow convergence at low energies, in particular for heavy syst ems characterized by a strong Coulomb field.