Coulomb potential screened self energy

We will show below that this correction term vanishes for the first-order self energy and cancels for the Coulomb-screened self energy. This is, however, not always the case for higher-order effects. As an example, for the self energy in an external magnetic potential the correction term gives rise to a finite shift... 

The self-energy determines the many-body accm acy for /rk), (k), thus G E). Following Hedin [7] and Hedin and Lundquist [8], E Ef is expanded in terms of a screened potential W, rather than the bare Coulomb potential v (atomic units are used throughout) ... 

To calculate the screening corrections of the self energy due to an external Coulomb potential, I4(r), we treat this potential as a perturbation of the first-order self energy [13]. This perturbation will affect the binding energy of the bound electron, the wave function and the bound-electron propagator... 

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. 

Fig. 5.2. Flow diagram sketching the practical implementation of the GW method. The partially self-consistent GWo updates the self-energy operator S, whereas the fully self-consistent GW also updates the screened Coulomb potential W...

Fig. 5.7. Diagrammatic representation of the self-energy and the screened Coulomb potential in (a) the fully self-consistent GW approximation, (b) the partially self-consistent GlVo approximation, and (c) the GofPo approximation. The generating functional

A many-electron method to calculate excitation energies in semiconductors and insulators. It uses a Green s function (G) and a screened Coulomb potential (denoted W) to express the so-called self-energy operator. The self-consistent solution of quasi-particle equations containing the self-energy operator gives quasi-particle energies which can be interpreted as... 

Calculated from first principles LMTO basis widi die ASA and die self-energy correction within die Green function and the screened Coulomb potential approximation (GWA) [68]. 

---