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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
##### Keywords:
two-body initial state
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