Self-energy part

Calculation of the self-energy part of the Lamb shift... 

VP vacuum polarization SE self-energy part of the Lamb shift LS = VP + SEE Lamb shift RC nucleus recoil correction, polarization Relativistic PT accounts for the main relativistic and correlation effects HOPT higher-order PT contributions. Data are from refs [1-10]. 

However, this ceases to hold when Gd contains also the self-energy part due to interactions. Using an approximate solution [13] for Gd for an electron-phonon interaction linear in the boson coordinates, one finds [11] that to lowest-order in the electron-phonon coupling aq 2, Ipc = Ipc + AIpc, with... 

This does not form the entire ( dressed ) perturbation because, in case the electron density changes to the first order in the above perturbation, the Fock operator acquires additional perturbation through the variation of its self-energy part, which leads to the self-consistent perturbation. Thus the perturbed Fock operator can be written as ... 

We separate from the expression for the self-energy part of the one-loop correction (7) the function... 

The propagator [6-9] or Green s function method (GFM) [10-14] provides another approach to calculate the quasi-particle energy bands. The Dyson equation provides the exact E(N 1) energies in a formally one-particle picture, but the equation can only be solved approximately in real applications [57], With the irreducible self-energy part in the diagonal approximation being correct to second-order, the inverse Dyson equation can be written as [26]... 

One can also extend the RPAE by including the self-energy part of the photoelectron s interaction (SEP). In lowest order, this correction is... 

Dependence of Ab Initio and Semiempirical Ionization Potentials on Order of Perturbation Correction of Self-energy Part... 

SEMIEMPIRICAL IONIZATION POTENTTALS ON ORDER OF PERTURBATION CORRECTTON OF SELF-ENERGY PART... 

OVGF(af initio) results were obtained using only second- and third-order perturbation corrections for the self-energy part. 

Self-energy part with only the second-order perturbation correction. 

Self-energy part with second- and third-order perturbation corrections. 

Here, e denotes the diagonal matrix of all one-particle (orbital) energies and 2(oo) stands for the static self-energy matrix. We recall that the latter can be computed exactly once the dynamic self-energy part is known. The one-particle GF is determined as the upper left block of the inverse of the matrix T(l — A. More precisely... 

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