Radiative self-energy

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 ... 

The contributions that have been considered in order to obtain precise theoretical expressions for hydrogenic energy levels are as follows the Dirac eigenvalue with reduced mass, relativistic recoil, nuclear polarization, self energy, vacuum polarization, two-photon corrections, three-photon corrections, finite nuclear size, nuclear size correction to self energy and vacuum polarization, radiative-recoil corrections, and nucleus self energy. 

Abstract. The second-order electron self-energy is evaluated to all orders in the interaction with the Coulomb field of the nucleus for the ground state of hydrogen-like uranium ions. This completes the nonperturbative calculation of radiative corrections of order a2. The major theoretical uncertainty is eliminated which provides predictions of the ground-state energy with a relative accuracy of about 1(P6 for the uranium system. This allows for high-precision tests of QED in the strong field of the nucleus that are expected to be available experimentally in the neax future. 

The complete set of second-order radiative corrections are displayed in Fig. 1. These diagrams are naturally divided into separately gauge invariant subsets SESE a),b),c), VPVP d),e),f), SEVP g),h),i) and S(VP)E k). The abbreviation SE stands for self energy and VP denotes vacuum polarization. Most of these corrections have been already calculated numerically for 238U91+ and 208Pb81+ ions (see the latest reviews in [2,3]). 

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

Self energy and vacuum polarization of order a and the nuclear size account for the measured Lamb shift in hydrogenlike heavy ions at the current level of accuracy. Radiative corrections of the order contribute to the Lamb shift of the lsi/2 state and amount to about 1 eV for uranium. Facing higher precision in experiments, these corrections have to be evaluated to yield a reliable Lamb shift calculation. 

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] ... 

Fig. 1. Feynman graphs that describe radiative corrections in one-electron ion with the electron in the state A. The graph a) describes the electron self-energy (SE) and the graph b) describes the vacuum polarization (VP). Notations are given in the text.

Figure 18. Typical higher-order radiative diagrams for the screening corrections to the self-energy and vacuum polarization.

The Breit corrections are sometimes classified as nonradiative effects in contrary to the radiative affects which are true quantum-electrodynamical effects due to the electron self energy and vacuum polarization [30-32]. 

The simplest radiative correction is due to ff self-energy loops in the photon propagator. Their effect can be taken into account by defining a running or effective coupling constant a ) which depends upon the carried by the photon line when it couples to a charged fermion. (This concept is treated in Section 21.7.) Thus one should use... 

The procedure sketched above has recently been applied to the ground state of medium-heavy helium-like ions. We have evaluated the effect of QED combined with electron correlation, defined as the interaction with at least two Coulomb interactions. The QED part is here restricted to first order and consists of non-radiative effects (retardation of the electromagnetic interaction and effect of virtual electron-positron pairs) as well as radiative effects (electron self-energy, vacuum polarization and vertex correction). 

The fluorescence quenching occurs when dye molecules are close to the metal. The energy from the first excited fluorophores can be consumed through a non-radiative path to the metal. A spacing layer is usually required to avoid this energy transfer process. In addition, the concentration of the dispersed dye molecules should be suitable to avoid self quenching [34, 81]. 

Emission inner filter effect (self-absorption) The fluorescence photons emitted in the region overlapping the absorption spectrum can be absorbed (radiative energy trans-... 

---