Iterative solution of multichannel three-body equations

Abstract

A recently proposed method for solving scattering equations is generalized to the case of multichannel scattering equations. In the present work we write the final result of the method for multichannel scattering equations in such a way that it has all the important features of a related method for single channel Lippmann-Schwinger-type equations proposed by Kowalski and Noyes but is more general in practice. The method relies on the introduction of an auxiliary equation containing an arbitrary function. The kernel of the auxiliary equation is in general weaker in nature than the original kernel and hence the auxiliary equation is expected to have a (rapidly) convergent iterative solution. It is suggested that the method could be an efficient method for solving three-body scattering equations. Using the iterative solution of the auxiliary equation, the method is used numerically to compute fully off-shell $t$ matrix elements for the spin doublet and the spin quartet neutron-deuteron scattering in the Amado model. The iterative solution of the auxiliary equation is found to converge significantly faster than the conventional Pad\'e technique-an unexpected result-if the freedom in the choice of the arbitrary function is exploited.NUCLEAR REACTIONS Multichannel scattering equations, iterative solution, spin \textonehalf{} and spin $\frac{3}{2}$ neutron-deuteron scattering, Amado model, off-shell $t$ matrix elements and phase shifts computed.