A novel computational approach for study of proton-proton scattering

In this paper, we have implemented a novel computational approach to study proton-proton scattering. The approach is applicable to all charged particle scattering scenarios and solves the challenge of incorporating the long-range Coulomb interaction alongside the short nuclear interaction using the phase function method. The key idea is to construct a reference potential using three smoothly joined Morse functions that collectively capture both nuclear and electromagnetic interactions. The reference potential is utilized in solving the phase equation which is derived by the transformation of the Schrodinger equation, for obtaining the scattering phase shifts for different values of orbital angular momentum called as ℓ-channels (S, P, D, F, G, H). The parameters of reference potential are optimized to minimize the Mean Squared Error between obtained and expected phase shifts, resulting in the construction of inverse potential for various ℓ-channels of the proton-proton system. Utilizing the phase shifts obtained from the inverse potentials, we have calculated the total cross-section and the low energy effective-range parameters, which have been found to be in excellent match with the experimental data.