Basis-independent multiple-scattering theory for electron spectroscopies:: General formalism

I present here a general formalism that allows the construction of the cross section of any electron spectroscopy in a straightforward and transparent way. This approach does not make any assumption concerning the choice of the basis functions used to expand the wave function of the electron. In this sense, it generalizes existing theories. It allows us to keep the physics well in view and offers, due to the relationship between operators and parts of a pictorial representation of the experiments, a type of a graphical interface to the problem at hand. Moreover, it does not assume any particular shape for the potential.