One-dimensional three-body scattering problem used as a testing ground for the K-matrix method for scattering reactions of complex systems
Tandon, Gaurav K.
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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.