Dispersion Relations for Three-Particle Scattering Amplitudes. III.

We continue our discussion of the scattering of three nonrelativistic, spinless particles interacting via two-body Yukawa potentials. We study the on-energy-shell amplitudes for the breakup of a two-particle bound state, for elastic scattering off a bound state, and for rearrangement as a function of the total center-of-mass energy $E$ for fixed physical values of the angle variables. We show that each of these amplitudes is given by a "Fredholm series" which is uniformly convergent with respect to $E$ for all values of $E$ on the physical sheet including the real axis. We also show that each of these amplitudes satisfies a dispersion relation in $E$ for fixed physical values of the angle variables. Except for simple poles which arise from the lowest-order diagrams, all of the singularities lie on the real $E$ axis.