Inner shell collective effects

One of the necessary conditions for a many-body description is the validity of the decomposition of the system under consideration on separate subsystems. In the case of very large collective effects we cannot separate the individual parts of the system and only the total energy of the system can be defined. However, in atomic systems the inner-shell electrons are to a great extent localized. Therefore, even in metals with strong collective valence-electron interactions, atoms (or ions) can be identified as individuals and we can define many-body interactions. The important role in this separation plays the validity for atom- molecular systems the adiabatic or the Born-Oppenheimer approximations which allow to describe the potential energy of an N-atom systeni as a functional of the positions of atomic nuclei. 

Collective effects near threshold in inner shell photoionization include along with RPAE corrections also relaxation processes. They are a consequence of the fact that near inner shell threshold the photoelectron leaves the atom slowly and all other electrons have sufficiently time to feel the field of the vacancy created as well as its decay-Auger or radiative. It is very essential that because the field variation takes place after vacancy creation, the photoelectron wave function must be ortogonalized to all other electron states of the atom - otherwise it includes the interaction with the final state of the ion before its formation. 

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