Convergence of the Sasakawa Expansion for the Scattering Amplitude

Sasakawa has rewritten Schr\"odinger's integral equation in such a manner that the inhomogeneous term has the asymptotic behavior of the exact scattering wave function. This paper gives a proof that the iterative solution for the scattering amplitude converges for all local potentials for which the function rV(r) is absolutely integrable. Under very general conditions the kernel of the Sasakawa equation is a Hilbert-Schmidt kernel. The integral equation is convenient for numerical solution in both the radial representation and the momentum representation.