Electron propagator pole structure

A similar analysis may be carried out for the electron detachment poles as well and the Auger poles (Eq — E 1( )) will obviously be found in the first quadrant of the complex E-plane. With this brief discussion of the pole structure of the complex scaled electron propagator as a common background, its utility in direct and simultaneous treatment of resonances of N+l electron and N-l electron systems becomes manifest e.g., for Be both Be+ (Is-1) 2S Auger and 2P Be- shape resonances have been calculated simultaneously from a single calculation on Be/25,26/. 

The structure of the p-p propagator is very similar to that of G. This popagator describes the simultaneous annihilation of two electrons from the system as well as the simultaneous attachment of two electrons to the system. In particular, the pole positions of the first and second part of FI represent double ionization potentials (DIP) and double attachment energies. DIPs, EAs, and IPs are, of course, important quantities of electronic systems. But not only the pole positions are related to experiment. The residue amplitudes and contain relevant information on the single and double ionization and attachment (or scattering) processes. For instance, the partial-channel photoionization cross section for production of molecular ions in the nth state reads in the sudden approximation ... 

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