Reaction mechanism in odd-even staggering of reaction cross sections

It was recently suggested that the odd-even staggering of reaction cross sections is evidence of the pairing anti-halo effect on projectile radii. We define the dimensionless staggering parameters Γ_rds and Γ_R for projectile radii and reaction cross sections, respectively, and analyze the relation between Γ_rds and Γ_R for the scattering of 14^,15^,16C from a 12C target at 83 MeV/nucleon by taking account of projectile-breakup and nuclear-medium effects with the microscopic version of the continuum discretized coupled-channels method. The value of Γ_R deviates from that of Γ_rds by the projectile-breakup effect, the nuclear-medium effect, and an effect resulting from the fact that the scattering is not exactly black-sphere scattering (BSS). The projectile-breakup and nuclear medium effects nearly cancel for Γ_R at low incident energies. The remaining non-BSS effect becomes small as the incident energy decreases, indicating that nucleus-nucleus scattering at lower incident energies can be a good probe for evaluating Γ_rds from measured reaction cross sections.