Alternative to Padé technique for solving scattering integral equations

Abstract

The aim of this work is to show how we can improve systematically the rate of convergence of a recently proposed method for iterative solution of scattering integral equations. The method relies on the introduction of an auxiliary equation containing an arbitrary function, whose kernel is much weaker than that of the original equation. The solution of the original equation is then expressed in terms of that of the auxiliary equation which is supposed to have a convergent iterative solution. In this work we introduce successive subtractions in the kernel in order to make it weaker. Such subtractions in the kernel are very simple to implement in practice and the present method appears to have some advantage over the other existing methods. We explain how to generalize the method for multichannel scattering equations. Using the present method we show how to modify a method by Fuda for three-particle scattering equations in order to have a method which uses the iterative solution only of nonsingular equations above the three-body breakup threshold. The method is used numerically to compute phase shifts, scattering lengths, and fully off-shell $t$ matrix elements for neutron-deuteron scattering in the $s$-wave Amado model and for nucleon-nucleon scattering with the Reid $^{1}S_{0}$ potential. The iterative solution of the auxiliary equation is found to converge much faster than the conventional Pad\'e technique in the case of the neutron-deuteron scattering and yields results with high precision.[NUCLEAR REACTIONS Multichannel scattering equations, iterative solution of auxiliary equations, Reid $^{1}S_{0}$ potential, Amado model, off-shell $t$ matrix elements and phase shifts computed.]