A semiclassical formula for the reaction cross-section of heavy ions

We discuss an improvement to the expression for the heavy-ion reaction cross-section proposed long ago by Karol (P.J. Karol, Phys. Rev. C 11, 1203 (1975)) which describes the two-ion interaction through the nucleon-nucleon collisions in their overlap region when they come into contact. This improvement consists in considering the limitations due to the Pauli principle, which at low incident energies forbids many nucleon interactions, and in including a Coulomb factor. The final expression for which we also propose a new parametrization reproduces satisfactorily the known reaction cross-sections for many ion combinations using a global set of parameters. A decomposition of the reaction cross-section into the contributions of peripheral interactions, as a function of the impact parameter, is also discussed.