Asymptotics of the binary amplitude for a model Faddeev equation

Abstract

A model equation obtained from the s-wave Faddeev equation in configuration space for three identical bosons by replacing the inhomogeneous integral term with a known function is studied. This function simulates the asymptotic decrease of the inhomogeneous term in the original Faddeev equation when y → ∞ as ∼y^–3/2. The asymptotes of the amplitude functions that approach the scattering amplitudes when y → ∞ are obtained analytically for the model equation using the Green function. It is shown that the asymptotics of the binary channel amplitude function oscillates. The similar oscillating behavior of the binary amplitude function is numerically demonstrated for the original s-wave Faddeev equation describing the neutron–deuteron scattering process.