Approximation Techniques in Three-Body Scattering Theory

With the aid of some operator algebra the Lippmann-Schwinger integral equations for three-body transition amplitudes are recast in a form which involves two-body transition operators rather than two-body potentials. These equations, which are uncoupled and apply to all channels, are ideally suited to be the basis for approximation schemes, of the impulse approximation type, which have the distinctive feature of preserving unitarity. Two such approximations are described. With either of these as the leading term, a method of successive approximations is developed which yields an expansion for the exact amplitude whose convergence properties are expected to be considerably improved over the usual Born and multiple-scattering expansions. At high energies and low momentum transfers we obtain a unitary version of the strip approximation. Here the integral equation is quite tractable and represents the nondispersion-theoretic analog of multiparticle N/D techniques which have been applied recently to N-N and π-N reactions.