  The electron and photon transport processes in spectroscopy techniques
described by the invariant embedding theory is here revisited. We report a
convergence method to obtain closed analytical solutions to the 3D
integro-differential equations. This method was successfully used in
calculating the dependence of the electron backscattered fraction on the atomic
number and on the energy. Also the fraction of absorbed electron as a function
of incident angles was calculated. Using a states ladder model for the electron
energies, this method provides a tool for testing physical parameters involved
in the transport theory, such as the elastic and inelastic cross sections. The
outstanding feature of the invariant embedding differential equations of
considering observable quantities (such as the emergent flux of particles) as
independent variables makes them a suitable tool to describe experimental
situations.
