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Annales Henri Poincaré

, Volume 16, Issue 11, pp 2569–2602 | Cite as

Inverse Scattering at High Energies for Classical Relativistic Particles in a Long-Range Electromagnetic Field

  • Alexandre JollivetEmail author
Article
  • 43 Downloads

Abstract

We define scattering data for the relativistic Newton equation in a static external electromagnetic field \({(-\nabla V, B)\in C^1(\mathbb{R}^n,\mathbb{R}^n)\times C^1(\mathbb{R}^n,A_n(\mathbb{R})), n\geq 2}\), that decays at infinity like \({r^{-\alpha-1}}\) for some \({\alpha\in (0,1]}\), where \({A_n(\mathbb{R})}\) is the space of \({n\times n}\) antisymmetric matrices. We prove, in particular, that the short-range part of \({(\nabla V,B)}\) can be reconstructed from the high-energy asymptotics of the scattering data provided that the long-range tail of \({(\nabla V,B)}\) is known. We consider also inverse scattering in other asymptotic regimes. This work generalizes [Jollivet (Asympt Anal 55:103–123, 2007)] where a short-range electromagnetic field was considered.

Keywords

Dirac Operator Inverse Scattering Born Approximation Radial Part Small Angle Scattering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Paul Painlevé, CNRS UMR 8524Université Lille 1 Sciences et TechnologiesVilleneuve d’Ascq CedexFrance

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