Perturbation theory screened Coulomb potentials

We now have equations of motion for the one- and two-particle Green s functions. They depend on the Hartree-exchange-correlation self-energy. Its Hartree part is trivial, but a practical way of calculating its exchange-correlation part is needed. Hedin [36] proposed a scheme that yields to a set of coupled equations and allows in principle for the calculation of the exact self-energy. This scheme can be seen as a perturbation theory in terms of the screened interaction W instead of the bare Coulomb interaction v. We show a generalization of this derivation for the case of a nonlocal potential. 

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