Physical Review C
The scattering reactions of three equal-mass particles constrained to move in a straight line and interacting with each other via zero-range potentials have been analyzed on the basis of the extended R-matrix theory. The simplicity of the model facilitates an exposition of the complexities that result from the existence of rearrangement channels and from the possibility for breakup into three-body channels. The conventional expressions for the K matrix and the T matrix are derived on a rigorous basis. A practical method for approximating the continuum of three-body breakup channels by a discrete set is used to carry out a distorted-wave Born approximation (DWBA) K-matrix calculation of the probabilities for transmission, knockout, and breakup when one particle is incident on a bound state of the other two. This method is found to give much better results than a DWBA T-matrix calculation.
Rodjak, D.; Tobocman, William; and Tandon, Gaurav K., "One-Dimensional Three-Body Scattering Problem Used As A Testing Ground For The K-Matrix Method For Scattering Reactions Of Complex Systems" (1972). Aerospace, Physics, and Space Science Faculty Publications. 395.