ABSTRACT
One of the aims of ELNES theory is to describe the energy transfer from a fast
incident electron (the probe) to a core electron of a particular atom belonging to a
solid target. In the target inertial frame, fast means that the electron velocity and
the light velocity have the same order of magnitude (v c). This energy transfer
results from the interaction of the core electron with the electromagnetic field
radiating from the fast incident electron. In the more familiar fields of quantum
chemistry or solid state physics, the interaction between a pair of valence electrons
can be accurately described by using a Coulombic potential, because the velocities
of these electrons are very small compared with c. The field radiating from each
electron is an irrotational electric field. This approximation is no longer valid in
ELNES, because one of both electrons of the pair is a fast electron. The interaction
between a fast electron and a core electronmust be described in the frame of special
relativity. It is clear that the electron probe in a TEM is always relativistic. The
faster is the electron probe, the more important are the relativistic corrections. This
chapter aims to give a relativistic approach to the electric dipole transition from an
atomic core level.
