The Chandler–Gibson theory of N-body scattering is used to define a new 𝒦 matrix for N-body quantum scattering systems. The half-on-shell 𝒦 matrix has the proper channel thresholds and may be computed using a 𝒦-matrix form of the CG equations. The on-shell 𝒦 matrix is an Hermitian matrix for all energies and is related to a unitary scattering matrix via a Cayley transform. A B-spline solution method is developed and applied to a two-body and a three-body test problem. The three-body numerical calculations are within 0.5% of the exact solution both below and above the breakup threshold.
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Gibson et al. (1991) studied this question.
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