Self-energy correction

The physical meaning of our final equation is best seen on eqn 39. The term containing w is essentially the self-energy correction introduced by Mulliken in his analysis of electronegativities to account for the average repulsion of electrons occupying the same orbital. In order to get an idea of the orders of magnitude, let us apply eqn 39 to a model computation of FeCO, made to compare the ClPSl results of Berthier et al. [11] with those of a simple orbital scheme. Consider one of the two x systems of FeCO, treated under the assumption of full localization (and therefore strict cr — x separation)... 

Mohr, P.J. (1992) Self-energy correction to one-electron energy levels in a strong Coulomb field. Physical Review A, 46, 4421-4424. 

In Eq. (9.21), the second summation is over lattice vectors H. The last two terms of this equation represent the (000) term in the Fourier summation and the self-energy correction. The latter describes the interaction of the point charge with itself, which, as noted above, is included in the reciprocal space summation and must therefore be subtracted. 

Our method of calculation is based on an idea by Ivanov-Ivanova [11]. In an atomic system, the radiative shift and the relativistic part of the energy are, in principle, determined by one and the same physical field. It may be assumed that there exists some universal function that connects the self-energy correction and the relativistic energy. The self-energy correction for the states of a hydrogen-like ion was presented by Mohr [1] as ... 

In particular we will show the dependence of the electronic gap on both wire size and orientation. Further, in some of the studied wires, self-energy corrections, by means of the GW method, and also electron-hole interaction, by solving the Bethe-Salpeter equation, will be included in order to have an appropriate description of the excited states. 

Figure 39 Band structure of the (a) fully saturated and (b) partially saturated Si[i]-SiC>2(0 01) SL projected along the two symmetry directions of the 2D Brillouin zone of the (0 01) surface. K and M represent, respectively, the k-points in the corner and in the middle of the side of the 2D Brillouin zone. A self-energy correction of 0.8 eV has been added to the conduction states. Energies (in eV) are referred to the valence band maximum.

Fig. 5. Feynman diagrams representing the self-energy correction in the presence of an additional screening potential Vc(r) (dashed line)...

These cases can be contrasted by most uranium intermetallics, which have Fermi surfaces in good agreement with LDA calculations which treat the f electrons as band states (IQ. In the one case where a mixed valent Fermi surface is known (CeSno), it is also in excellent agreement with an LDA f band calculation (T8-19L with a mass renormalization of five due to a self-energy correction resulting from virtual spin fluctuation excitations (2Q). Notice the different dynamic correlations used to explain the mass renormalizations in the f core and f band cases. 

In the present work we investigate a part of the two-loop self-energy correction to the Lamb shift in hydrogen, namely the irredncible part of diagram Fig. 1(a), referred to as the loop-after-loop correction. This contribntion has been the snb-ject of a recent debate in the literature. Analytic calculations of its. Za-expansion coefficients were carried out by Eides and co-workers [1] and Pachucki [2] in order a Za) and by Karshenboim [3] in order A direct numer-... 

The third and final term of the total multipolar Hamiltonian (6) is the interaction Hamiltonian. Excluding the transverse polarization term [17], which is important only when considering self-energy corrections, fhe coupling Hamiltonian is... 

The j H(S> associated with each radiation mode is the energy associated with the familiar vacuum fluctuations, the origin of spontaneous emission and self-energy corrections. The eigenstates m(k, X)) of Hmd are number states states that more closely model the coherence and other properties of laser light will be introduced later. 

As QED-radiative effects of coder a, we identify the formal expression for the self-energy correction... 

The most accurate calculations of the SE correction were carried out in Mohr (1974a, 1992) and in Indelicato and Mohr (1998) for the point nucleus, and in Mohr and Soff (1993) for the extended nucleus. For heavy systems (Z > 50) the dependence of the self-energy correction FSE on the nuclear radius R also Ahas to be taken into account (Soff 1993). 

Figure 5.14 EXAFS (top) and MEXAFS spectra (bottom) at the L2-edge of Pt in FejPt. Calculations for the ordered compound (full line), compared with the experimental data for the Feo.72Pto.28 (dashed line) (Ahlers 1998). The corresponding calculations for the scattering path operator thave been done using the matrix inversion technique for a cluster of 135 atoms in the XANES and 55 atoms in the EXAFS region, including the central absorber site. The effects of self-energy corrections (Fujikawa et al 1997 Mustre de Leon et al 1991) have been accounted for after calculating the spectra.

For a direct comparison of calculated spectra with experiment, these had to be shifted by about 2 eV, as indicated in the second panel of Figure 5.17. This finding is quite common and has to be ascribed to self-energy corrections. With this shift applied, the experimental spectra could be reproduced by the calculations in a rather satisfying way allowing for a detailed discussion of these. The observed main peak of the experimental spectra is found to be almost constant for the various photon energies... 

---