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Semi-classical asymptotics for total scattering cross sections of 3-body systems. (English) Zbl 0769.35045
One considers the total scattering cross section for a three-body quantum system with a two-body initial state as a function of the Planck constant \(h\). Under the assumption that pair potentials are \(O(| x|^{- \rho})\), \(\rho>5/2\), as \(| x|\to\infty\), it is shown that \(\sigma(h)\sim h^{-\kappa}\), \(h\to 0\), where \(\kappa=2(\rho-1)^{-1}\).

MSC:
35P25 Scattering theory for PDEs
81U10 \(n\)-body potential quantum scattering theory
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