Approximation Method for Three-Body Collisions

A new approximation for the three-body collision problem is described, which allows practical calculation of elastic, inelastic, rearrangement, and breakup amplitudes. The approximation is derived from a novel form of the Lovelace-Faddeev equations in which all two-body bound states appear explicitly. It appears in practice as a simple modification of the impulse-pickup approximation, and is expected to considerably extend the useful energy range of that approximation. It is shown that unitarity is satisfied within a certain approximation, and that the submatrix of the $S$ matrix that excludes the breakup channel satisfies a unitary constraint. The symmetry requirements for identical particles can be treated rigorously, and lead to a practical simplification of the method. Numerical calculations of bound-state scattering in an exactly soluble model show encouraging results.