Utility of nucleon-target profile function in cross section calculations

We test the utility of an effective nucleon (N)-¹²C profile function in calculating nucleus-¹²C optical phase shift function in the Glauber theory. A calculation of the complete Glauber amplitude is performed by using wave functions for ⁴He and ⁶He projectiles, leading to the reaction and elastic differential cross sections in good agreement with experiment. By relating the N-¹²C 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 ⁴He, ⁶He, ⁹Be, ¹²C, and ²⁷Al, we can reproduce cross sections measured at 800 MeV/nucleon to much higher accuracy than the optical limit approximation.