Higher quantum electrodynamic effects

The leading quantum electrodynamic effects to be accounted for in electronic structure calculations are the radiative corrections known as electron self-energy interaction and vacuum polarization. For the energy of electronic systems, the latter is usually small compared to the former, but only the latter can be expressed in terms of an effective additive potential to be included in the electronic structure calculations. The total vacuum polarization potential can be expanded into a double power series in the fine structure constant a and the external coupling constant Za. The lowest-order term, the Uehling potential, can be expressed as [110-112]  

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In this last section we mention a few cases, where properties other than the energy of a system are considered, which are influenced in particular by the change from the point-like nucleus case (PNC) to the finite nucleus case (FNC) for the nuclear model. Firstly, we consider the electron-nuclear contact term (Darwin term), and turn then to higher quantum electrodynamic effects. In both cases the nuclear charge density distribution p r) is involved. The next item, parity non-conservation due to neutral weak interaction between electrons and nuclei, involves the nuclear proton and neutron density distributions, i.e., the particle density ditributions n r) and n (r). Finally, higher nuclear electric multipole moments, which involve the charge density distribution p r) again, are mentioned briefly. 

DCB is correct to second order in the fine-structure constant a, and is expected to be highly accurate for all neutral and weakly-ionized atoms [8]. Higher quantum electrodynamic (QED) terms are required for strongly-ionized species these are outside the scope of this chapter. A comprehensive discussion of higher QED effects and other aspects of relativistic atomic physics may be found in the proceedings of the 1988 Santa Barbara program [9]. 

All the terms up to this point can be calculated to high precision, leaving a finite residual piece due to higher order relativistic and quantum electrodynamic effects which lie at the frontier of current theory. 

Scholes G D and Andrews D L 1997 Damping and higher multipole effects in the quantum electrodynamical model for electronic energy transfer in the condensed phase J. Chem. Phys. 107 5374-84... 

One should note that the relativistic effect on the core IPs can already be seen for Ne and progressively increases for heavier atoms. Thus, to compare theoretical results with the experimental data for the ionization core levels one needs to account for relativistic contributions even for relatively light systems. The still existing disagreement between the experimental data and theoretical lOTC results for the inner Is core IPs can be attributed to the neglection of other higher-order relativistic quantum electrodynamic contributions such as Breit, self energy and vacuum polarization terms [34]. 

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