Modified Glauber model for the description of elastic scattering between heavy ions

The standard form of the optical limit of the Glauber model used for the description of elastic scattering is modified to account for the Coulomb distortion of the trajectory occurring in the case of heavy ion scattering at relatively low bombarding energies. We retain the description of the process in terms of nucleon-nucleon collisions, but we relate the nuclear density overlaps for each partial wave to the distance of closest approach of the associated Rutherford trajectory, rather than to the asymptotic value of the impact parameter. Parameter-free predictions for the elastic scattering of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ at 390 MeV and of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ at 1760 MeV from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, based on experimental nucleon-nucleon total cross sections and standard densities, show a remarkable improvement for both differential and reaction cross sections. The consistency of the approach is strengthened by a correlated method for the inversion of the phase shifts, which, for the examined cases, yields optical potentials very similar to those obtained by optical-model fit analysis.