Total reaction cross section from the difference of the Rutherford and measured elastic cross sections

A model independent method of obtaining the total reaction cross section as a difference between integrals over solid angle of the Rutherford and measured elastic cross sections is proposed and discussed. The conditions for validity of the method are first that the measured differential cross section be Rutherford within experimental error at forward angles, and second, that the projectile be highly absorbed. Both conditions are fulfilled in a variety of experiments with complex projectiles. The method is applied to $\alpha$-particle scattering by ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{206,208}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. Limitations of the method, comparison with transmission, charge collection, and optical model methods, and applications to heavy ion scattering are discussed.