A few variations of the two potential formalism will be presented. Firstly, a new derivation of the standard two potential approach is given. Secondly, the proof of the previously proposed coupled channel approach is upgraded, and thirdly, a new distorted wave expression for the two potential problem is proposed. The new formalism is applied to the Coulomb-nuclear interference phenomena, paying due attention to the singularities of the Coulomb potential matrix element and scattering amplitude, and the finite size effect of interacting particles. To demonstrate the applicability of the new formalism, $\pi$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering differential cross sections are calculated.

NUCLEAR REACTIONS Two potential approach, new distorted wave integral equation, Coulomb-nuclear interference, calculated $\sigma \left(\theta \right)$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi , \pi )$.

• Received 18 November 1981

DOI:https://doi.org/10.1103/PhysRevC.26.1123