Hubbard-I approach to lanthanide photoemission spectra

Photoemission is a powerful spectroscopy of lanthanide systems (Campagna et al., 1979). This is due to the distinct atomic multiplet features, which serve as a fingerprint of the configuration adopted by the lanthanide ion in the solid environment. 

In photoemission, a photon y of energy hco impinges on a solid, which is an N-electron system in its groimd state IN 0). The photon is absorbed and its energy is transferred to an electron, which is emitted, leaving behind a solid with only N—1 electrons and in some excited state. Schematically, 

The energy of the electron, E, is measured and contains information about the excitation energies in the N—1 electron system  

In principle, all possible excitations contribute to the photoelectron spectrum and the proper quantum mechanical amplitude must be calculated. For the lanthanides, the atomic limit corresponds to the assumption that the photoelectron spectrum is dominated by those processes, where the photon hits a particular ion and causes an excitation on that ion without disturbing the remainder of the crystal. In the standard model, the lanthanide ion would initially be in its bivalent / configuration with the Hund s rule ground state multiplet (Table 1 in Section 2.2), and would be transferred into some multiplet within configuration 

In view of the strength of the Coulomb interaction, the atomic limit is certainly a quite idealized assumption. For example, in the real world, the kicked out electron still has some distance to travel through the solid before leaving at the surface and 

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