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

• Received 17 September 1999

DOI:https://doi.org/10.1103/PhysRevC.61.051601