The reaction cross section (σR) is calculated using the optical limit of the Glauber theory. A density-dependent effective nucleon-nucleon (NN) cross section σNN is considered. Finite and zero range NN interactions are studied. The effect of finite range and an appropriate local density can increase σR up to 20% compared to the zero range at constant density (0.16fm−3), while a zero range calculation with free NN cross section increases σR up to 13%. These factors affect the values of the rms radii for neutron rich nuclei extracted from σR.