Method of continued fraction and application to atomic physics

An iterative method for solving the scattering equations for local as well as nonlocal potential is proposed. The amplitude is presented in a form of continued fraction. The main features of our method are simplicity, extremly high efficiency and high accuracy. The matrix inversion or the computation of matrix elements are not required. For the N-rank separable potential, the N-th iteration of our method yields the exact result. By the Rayleigh-Schroedinger expansion, we can demonstrate the rapidity of convergence of our method. We applied this method to e-H scattering in the static exchange approximation. (orig.)