First order self energy

Fig. 3.22. Polarization insertion in the first order self-energy operator...

Hi) First-order self-energy and polarization operator... 

A description of the partial-wave renormalization (PWR), used for calculating the first-order self energy and certain higher-order effects for the energy levels in highly cllarged ions, is presented. We put special emphasis on correction terms which have to be considered due to the use of the non-covariant subtraction scheme used in PWR. 

In this paper, we investigate the correction terms obtained when applying a covariant Pauli-Villars regulator [16] when formulating the PWR procedure. In Section II we consider the first-order self energy and the Coulomb screened self energy is discussed in Section III. Finally, we derive an expression suitable for numerical evaluation of the correction term in the Coulomb screened case. 

We will show below that this correction term vanishes for the first-order self energy and cancels for the Coulomb-screened self energy. This is, however, not always the case for higher-order effects. As an example, for the self energy in an external magnetic potential the correction term gives rise to a finite shift... 

To calculate the screening corrections of the self energy due to an external Coulomb potential, I4(r), we treat this potential as a perturbation of the first-order self energy [13]. This perturbation will affect the binding energy of the bound electron, the wave function and the bound-electron propagator... 

The only difference between the first-order self energy correction and this wave function correction term is the appearance of (5a) instead of a). Thus, from this expression we can conclude that in the case of the first-order self energy the correction term vanishes. For the screening case only the first term vanishes and we are left with... 

B The dynamic particle-hole self energy C The zeroth-order degenerate states D First order self energy... 

---