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