Semi-classical asymptotics for total scattering cross sections of \(N\)-body quantum systems
type: Item
instance of: scholarly article
title: Semi-classical asymptotics for total scattering cross sections of \(N\)-body quantum systems
zbMATH Open document ID: 0851.35104
author: Hiroshi T. Ito
author: Hideo Tamura
published in: Osaka Journal of Mathematics
publication date: 1996-06-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 81U10
zbMATH DE Number: 871833
zbMATH Keywords: semiclassical estimates
zbMATH Keywords: total scattering cross sections
reviewed by: André Martinez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 871833