Many-body systems, optical potential

Shakeup represents a fundamental many-body effect that takes place in optical transitions in many-electron systems. In such systems, an absorption or emission of light is accompanied by electronic excitations in the final state of the transition. The most notable shakeup effect is the Anderson orthogonality catastrophe [5] in the electron gas when the initial and final states of the transition have very small overlap due to the readjustment of the Fermi sea electrons in order to screen the Coulomb potential of pho-toexcited core hole. Shakeup is especially efficient when the optical hole is immobilized, and therefore it was widely studied in conjunction with the Fermi edge singularity (FES) in metals [6-8] and doped semiconductor quantum wells [9-15]. Comprehensive reviews of FES and related issues can be found in Refs. [16,17]. 

The multiple scattering optical potential formalism of Watson [Wa 53] provides a formal solution of the nonrelativistic many-body Scluodinger equation for the projectile-nucleus system in terms of a systematic expansion in elemental, many-body operators defined in ref. [Wa53]. The many-body Schrodinger equation is... 

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