Range of validity of the eikonal approximation within the coupled-channel description of heavy-ion scattering processes

Abstract

Abstract. The validity of the eikonal approximation in heavy-ion reactions is systematically investigated for both potential scattering and coupled-channel processes. Simple prescriptions are advanced to account for Coulomb and nuclear distortions of the trajectory within the eikonal description. The strong nuclear absorption characterizing heavy-ion collision favours the extension of the limit of validity of the eikonal approximation to larger angles and to lower energies than probably expected, i.e. of the order of 30-40 MeV per nucleon in the case of elastic scattering or inelastic processes with very low excitation energies. In the case of inelastic excitation to highlying modes, and in particular at the lowest bombarding energies, the agreement between the eikonal predictions and the exact ones is worsened by the finite Q-values, but not invalidated if proper corrections for the momentummismatch are accounted for. A similar argument also applies to the strong-coupling situations, where the discrepancies are amplified by the multistep nature of the process.

Analysis of corrections to the eikonal approximation

“…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.…”

“…This correction applied to the sole Coulomb interaction has already given interesting results for Coulombdominated reactions in Refs. [23,31]. In this case, the distance of closest approach b ′ C can be derived analytically [15,23] …”

“…This semiclassical correction can also be generalized to both the nuclear and the Coulomb interactions [29,31]. Assuming that a real potential V is used to compute the trajectory, we can obtain the distance of closest approach b ′ by solving the following equation [15,22] …”

“…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.…”