Multiple scattering expansions for nonrelativistic three-body collision problems. Ii. Convergence of the faddeev-watson expansion for rearrangement collisions

Abstract

The convergence of the faddeev-watson multiple scattering expansion is investigated for three-body rearrangement collisions, 1+(2,3)=(1,2)+3, for systems with coulomb interactions and arbitrary masses. The matrix elements of the expansion are evaluated to the second order in the two-body t-matrix using the nutt procedures. The result suggests that the expansion for rearrangement transition amplitudes (psi₁⁽³⁾?t_r?psi₁⁽¹⁾) between ground two-body states converges in the high energy limit for a nonrelativistic three-body coulomb system with arbitrary masses. The effect of the constituent particle masses on the rate of approaching this high-energy behaviour is discussed. It is pointed out that the controversies regarding the role of proton-proton interaction in electron-transfer collisions for the (p⁺,h) system arise from the improper high-energy behaviour of the born series.