A Numerical Method for Solving the Lippmann- Schwinger Integral Equation with the Radial Interaction Potentials

In this article, a method is presented for transforming the singular Lippmann-Schwinger integral equation to a matrix algebraic equation. This method of computing the matrix elements of the reaction and transition operators is used on the real axis and on the complex plane, respectively. By specifying the elements value of the reaction and transition matrix on the energy-shell, both phase shifts and the differential scattering amplitudes and the differential cross sections are computable. The presented method for the Gaussian quadratures is suitably based on ALIREZA HEIDARI et al. 120 the Legendre, Laguerre, Hermite, Jacobi, Chebyshev, and shifted Chebyshev polynomials, and the selection of the nodal points and the weight functions is dependent on the physics of the problem considered and the user’s view.