Eikonal expansion for total cross sections of heavy ion reactions.

Abstract

We study the validity and convergence of the eikonal expansion for the calculation of total ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$ and total reaction ${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$ cross sections in the case of low-energy heavy-ion collisions. Investigations are performed by considering a few typical optical potentials, varying the incident energy from 10 MeV/nucleon to 300 MeV/nucleon. At low energy, the eikonal expansion does not necessarily converge and faces a violation of flux conservation, especially at low-impact parameter. For well-behaved cases, we find the eikonal approximation to be a convenient starting point. Adding the first correction leads in general to an acceptable accuracy with respect to the quantum mechanical result.