Photon propagator Coulomb gauge

Table 12.5 The oscillator strengths of the El transitions in Eul (Table 12.4) theoretical data - the Coulomb approximation method (columns A, B and C are corresponding to the gauges of the photon propagator Coulomb, Babushkin, Landau), multiconfiguration DF method (column D), experimental data (columns El, E2)...

DimipJ) is the transverse part of the photon propagator in the Coulomb gauge. In the coordinate representation it is... 

Taking into account electric nuclear transitions only, gives rise to a longitudinal part T>oo of the modified photon propagator, which reads in Coulomb gauge... 

It is therefore tempting to say that, to leading order in Cje2, but regardless of the relative speed, the effective interaction between, "1" and "2" is given by (2.5). However, suppose that instead one uses the Coulomb gauge for the photon propagator. Then one finds that (2.4) is replaced by... 

The causal photon propagator in Coulomb gauge can be defined, in a similar manner to (62), by... 

In Coulomb gauge the expression for the Coulomb photon propagator and for the transverse photon propagator are ... 

Even after the introduction of the no-pair approximation the physical background of the RDFT formalism outlined in this Section is not yet identical with that of the standard methods based on the no-pair DC- or DCB-Hamiltonian. In RDFT the complete electron-electron interaction via the photon propagator is taken into account both in the Hartree energy (58) and in the construction of approximations for Exc (see Appendix C). On the other hand, there is also no fundamental problem in restricting RDFT to the Coulomb or Coulomb-Breit level. Choosing Feynman gauge, the full D y, Eqs.(201),(202), reduces to... 

An analysis of the presented data shows that the Coulomb approximation results in different photon propagator gauges significantly differ from each other. In our approach, this difference is not more than 0.1% for different gauges. The contribution provided by the polarization and screening effects is very important for Eul ( 35%). In Table 12.6, we present theoretical and experimental data for the oscillator strengths of the ytterbium Ybl low-lying states (from Refs.[l, 2, 21]). The presented data confirm a complexity of the studied atom. The simple Coulomb approximation may hardly provide the necessary accuracy. 

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