Semi-classical asymptotics for total scattering cross sections of \(N\)-body quantum systems (Q1911593)

The authors consider the total scattering cross sections of \(N\)-body systems, when the incoming channel corresponds to a two-cluster decomposition of type \(\{1,(2, 3,\dots, N)\}\). The pair potentials are assumed to be smooth, and to decay like \(r^{- \rho}\) at infinity with \(\rho> 2\). If \(h\) denotes the Plank constant, they show that such a total scattering cross section behaves like \(h^{- 2(\rho- 1)}\) (in a distributional sense) as \(h\) tends to zero. This result extends a previous work of the authors, where only the case \(\rho> 5/2\) was considered.