Utility of nucleon-target profile function in cross section calculations

We test the utility of an effective nucleon (N)-C-12 profile function in calculating nucleus-C-12 optical phase shift function in the Glauber theory. A calculation of the complete Glauber amplitude is performed by using wave functions for He-4 and He-6 projectiles, leading to the reaction and elastic differential cross sections in good agreement with experiment. By relating the N-C-12 profile function to the NN profile function, we derive a new, simple formula to calculate reaction cross sections which requires only nuclear densities as an input. By applying this formula to various combinations of He-4, He-6, Be-9, C-12, and (27)AI, we can reproduce cross sections measured at 800 MeV/nucleon to much higher accuracy than the optical limit approximation.