Structures of S-matrices for three body Schrödinger operators. (English) Zbl 0748.35026

Summary: Structures of the \(S\)-matrix associated with the collision process from 2 clusters to 3 clusters are studied. This \(S\)-matrix is shown to have a continuous kernel except for 2-dimensional spheres on which 2-body subsystems have zero velocity. On these spheres, the \(S\)-matrix has, in general, singularities whose existence arises from the zero eigenvalues and the zero resonances of the 2-body subsystems.


35P25 Scattering theory for PDEs
81U20 \(S\)-matrix theory, etc. in quantum theory
35Q40 PDEs in connection with quantum mechanics
47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
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