Comments on the Faddeev Approach to Three-Particle Coulomb Systems

Expressions correlating the transition operators to Faddeev's $T^{\mathrm{}\left(i\right)\mathrm{}}$'s are given for a three-body scattering problem. Using the results of Ball, Chen, and Wong, a revised partial-wave analysis for various transition processes in a three-particle Coulomb system is suggested. Some of the apparent contradictions between the off-shell two-particle partial-wave $T$ matrix derived by Ball et al. and the full two-particle Coulomb $T$ matrix derived by Nutt are resolved. In an Appendix, it is shown that $T^{\mathrm{}\left(i\right)\mathrm{}}$ is related to the transition operators. This establishes the equivalence between the limiting procedure of Ball et al. and the conventional procedure for obtaining the transition amplitudes.