Utility of nucleon-target profile function in cross section calculations

Abstract

We test the utility of an effective nucleon $(N){\ensuremath{-}}^{12}\mathrm{C}$ 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 $N{\ensuremath{-}}^{12}\mathrm{C}$ 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.