Fermi Sea Correlation Effects

In the one-electron picture the photoelectron spectrum thus consists of a number of sharp peaks (Fig. 4 d), one for each core level, with the binding energy given by the negative of the HF eigenvalue (Koopmans theorem261). 

The 6-function in Eq. (3) contains information about the energy level structure and represents the simplest example of a spectral function for a core hole. By defining the spectral function Aj (e - to) as 

This result is actually valid far beyond the one-electron approximation because in the presence of interaction between the core hole and the surrounding electron cloud the spectral function Ai(e-co) will describe the full core level spectrum with shifted and broadened main lines, satellite lines and continua. 

For a deep core hole in the XPS regime it is quite reasonable to explain the breakdown of the one-electron approximation in terms of interaction between the core hole and the average electronic medium. However, for core holes in the outer shells, Fermi sea correlations can give significant contributions to satellite spectra and for low photoelectron energies interactions between the photoelectron and the residual ion can become important. In the rest of this section several of these aspects will be illustrated. 

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Fig. 5a-c. Fermi sea correlation effects pictured in (a) real space , (b) one-electron level scheme and (c) Feynman diagram... 

Fig. 6a-e. Fermi sea correlation effects in photoionization (a) One-electron level scheme, (b)—(d) Feynman diagrams describing monopole (K = 0), dipole (K = 1) and quadrupole (K = 2) fluctuation (correlation) processes and (e) schematic pictures of the resulting photoelectron spectrum... 

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