Self energy, atomic

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. 

The Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

GY noticed that the polarizability of an atom is approximately an exponential function of charge, and that the polarizability correction provided by the CPE expansion for an isolated atom was equal to the inverse of the Coulomb self energy of the... 

The P3 approximation to the self-energy was applied to the atoms Li through Kr and to neutral and ionic molecular species from the G2 set [47]. For the atoms, a set of 22 representative basis sets was tested. Results for the molecular set were obtained using standard Pople basis sets as described below. 

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) ... 

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 ... 

One may speak of the "classical radius of the electron," a = e1/mc2. derived by setting the self-energy of the coulomb field of a charge e contained at a radius a equal to Ihe relativistic re si energy, me2 of the electron. This a - 2.82 x 10" cm, comfortably smaller than any atom, but larger than the usual estimates of sizes uf protons and neutrons. 

We applied the generating functional approach to the periodic Anderson model. Calculation of the electron GFs gdd, 9ds, 9sd and gss reduces to calculation of only the d-electron GF. For this, an exact matrix equation was derived with the variational derivatives. Iterations with respect to the effective matrix element Aij(to) allow to construct a perturbation theory near the atomic limit. Along with the self-energy, the terminal part of the GF Q is very important. The first order correction for it describes the interaction of d-electrons with spin fluctuations. In the paramagnetic phase this term contains a logarithmic singularity near the Fermi-level and thus produces a Kondo-like resonance peak in the d-electron density of states. The spin susceptibility of d-electrons... 

Fig. lla-e. Monopole relaxation in response to a localized core hole (a) general self-energy diagram (b) monopole part of (a) (c) real space picture of monopole relaxation, illustrating the radial contraction of a relaxing shell typical core level spectra in (d) atoms and molecules and (e) metals... 

So far, we have fairly extensively discussed the general aspects of static and dynamic relaxation of core holes. We have also discussed in detail methods for calculating the selfenergy (E). Knowing the self-energy, we know the spectral density of states function A (E) (Eq. (10)) which describes the X-ray photoelectron spectrum (XPS) in the sudden limit of very high photoelectron kinetic energy (Eq. (6)). We will now present numerical results for i(E) and Aj(E) and compare these with experimental XPS spectra and we will find many situations where atomic core holes behave in very unconventional ways. 

Im. Z i(E) can be considered as a product of an ionic excitation density of states and an energy-dependent coupling constant. In model calculations one can independently vary the shape and the band with of the denstiy of states and the strength of the coupling constant. In the present case we can only vary these parameters indirectly by changing the atomic number Z. Since the self-energy involves the polarizability of the ionic system there must be an oscillator-strength sum rule such that... 

QED contributions to the Lamb shift consist of electron self-energy and vacuum polarization terms. In one-electron atoms the former is both the larger and the more difficult to calculate and has been the focus of much recent theoretical work. Up to Feynman diagrams including two-loops the self-energy contribution to a hydrogenic energy level can be written as [32]... 

Table 3. The contribution of the combined self-energy vacuum-polarization diagram for the ground state of hydrogenlike atoms expressed in terms of the function G(Za) defined by Eq. (2)...

---