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

Abstract

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

Analysis of corrections to the eikonal approximation

“…Wallace explicitly derived the first three orders of the correction [24][25][26]. However, our analysis, like others [27][28][29], has shown that only the first order is significant; it is given by…”

“…The encouraging results obtained in Ref. [29] for structureless nuclei suggest that it can be generalized to collisions involving more complex structures such as halo nuclei.…”

“…Unfortunately, the eikonal approximation is not valid at low energy: in that case, the assumption of a straight-line trajectory for the projectile does no longer hold because the deflection of the projectile by the target has to be properly taken into account. In the present paper, we study and compare two corrections that aim at improving the relative motion between the projectile and the target within the eikonal model [15,22,24,25,29,31,33].…”

“…However, at low energy, the deflection can no longer be neglected. At the first order, this can be corrected by replacing the impact parameter b by the actual distance of closest approach b ′ of the corresponding classical trajectory [15,22,29,31]. For a collision dominated by the repulsive Coulomb interaction, that distance will be larger than b.…”

“…Since this combination of both corrections does not provide a very consistent model, we study the extension of the semiclassical correction to the nuclear interaction [29,31,32]. The encouraging results obtained in Ref.…”