  We obtain an explicit formula for the diagonal singularities of the
scattering amplitude for the Dirac equation with short-range electromagnetic
potentials. Using this expansion we uniquely reconstruct an electric potential
and magnetic field from the high-energy limit of the scattering amplitude.
Moreover, supposing that the electric potential and magnetic field are
asymptotic sums of homogeneous terms we give the unique reconstruction
procedure for these asymptotics from the scattering amplitude, known for some
energy $E.$ Furthermore, we prove that the set of the averaged scattering
solutions to the Dirac equation is dense in the set of all solutions to the
Dirac equation that are in $L^{2}\left( \Omega\right) ,$ where $\Omega$ is any
connected bounded open set in $\mathbb{R}^{3}$ with smooth boundary, and we
show that if we know an electric potential and a magnetic field for
$\mathbb{R}^{3}\setminus\Omega$, then the scattering amplitude, given for some
energy $E$, uniquely determines these electric potential and magnetic field
everywhere in $\mathbb{R}^{3}$. Combining this uniqueness result with the
reconstruction procedure for the asymptotics of the electric potential and the
magnetic field we show that the scattering amplitude, known for some $E$,
uniquely determines a electric potential and a magnetic field, that are
asymptotic sums of homogeneous terms, which converges to the electric potential
and the magnetic field, respectively. Moreover, we discuss the symmetries of
the kernel of the scattering matrix, which follow from the parity,
charge-conjugation and time-reversal transformations for the Dirac operator.
