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The electron and photon transport processes in spectroscopy techniquesdescribed by the invariant embedding theory is here revisited. We report aconvergence method to obtain closed analytical solutions to the 3Dintegro-differential equations. This method was successfully used incalculating the dependence of the electron backscattered fraction on the atomicnumber and on the energy. Also the fraction of absorbed electron as a functionof incident angles was calculated. Using a states ladder model for the electronenergies, this method provides a tool for testing physical parameters involvedin the transport theory, such as the elastic and inelastic cross sections. Theoutstanding feature of the invariant embedding differential equations ofconsidering observable quantities (such as the emergent flux of particles) asindependent variables makes them a suitable tool to describe experimentalsituations.

Convergence method for calculating solutions to the 3D invariant embedding integro-differential equations describing electron transport processes