  It was recently suggested that the odd-even staggering of reaction cross
sections is an evidence of the pair- ing anti-halo effect on projectile radii.
We define the dimensionless staggering parameters, {\Gamma}rds and {\Gamma}R,
for projectile radii and reaction cross sections, respectively, and analyze the
relation between {\Gamma}rds and {\Gamma}R for the scattering of 14,15,16C from
a 12C target at 83 MeV/A by taking account of projectile-breakup and nuclear-
medium effects newly with the microscopic version of the continuum discretized
coupled-channels method. The value of {\Gamma}R is deviated from that of
{\Gamma}rds by the projectile-breakup effect, the nuclear-medium effect and an
effect due to the fact that the scattering are not the black-sphere scattering
(BSS) exactly. The projectile-breakup and nuclear medium effects are nearly
canceled for {\Gamma}R. The remaining non-BSS effect becomes small as an
incident energy decreases, indicating that nucleus-nucleus scattering at lower
incident energies are a good probe of evaluating {\Gamma}rds from measured
reaction cross sections.
