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


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.


Dirac Operator Inverse Scattering Born Approximation Radial Part Small Angle Scattering 
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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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