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We define scattering data for the relativistic Newton equation in an electricfield $-\nabla V\in C^1(\R^n,\R^n)$, $n\ge 2$, and in a magnetic field $B\inC^1(\R^n,A_n(\R))$ that decay at infinity like $r^{-\alpha-1}$ for some$\alpha\in (0,1]$, where $A_n(\R)$ is the space of $n\times n$ antisymmetricmatrices. We provide estimates on the scattering solutions and on thescattering data and we prove, in particular, that the scattering data at highenergies uniquely determine the short range part of $(\nabla V,B)$ up to theknowledge of the long range tail of $(\nabla V,B)$. The Born approximation atfixed energy of the scattering data is also considered. We then change thedefinition of the scattering data to study their behavior in other asymptoticregimes. This work generalizes [Jollivet, 2007] where a short rangeelectromagnetic field was considered.

On inverse scattering at high energies for the multidimensional relativistic Newton equation in a long range electromagnetic field