Many-body theory of electron scattering by excited atomic targets: Fundamental formulas

A many-body theory of electron-impact excitation out of excited atomic states is presented. After the fundamental equations and formulas of the general theory are given, first- and second-order approximations are introduced. In the case of the first-order theory, detailed analytical formulas are also developed. The physical interpretation of the first- and second-order theories are presented with the aid of Feynman-type diagrams. Following a discussion of initial- and final-state effects, the many-body theory is also related to the distorted-wave approximation.