Electron Self-Energy

Here i means NOT i and a are the electron self-energy from leads. 

A recent calculation has substantially reduced the uncertainty of the contribution of the second-order one-photon electron self energy to the energy level of the IS state. In general, this contribution can be expressed as... 

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]... 

The results for the fine structure measurements in N5+, F7+ and Mg10+ are summarized in table 4. In fig. 11 they are compared with theory and other precision measurements Z < 12. The scaling factor Z(Z — l)5a7mec2 is the order of the spin-dependent part of the one-electron self-energy [88]. As the figure shows, the sensitivity of the recent measurements to QED corrections of this order, matches or exceeds that of the high precision measurements in helium. 

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. 

Fig. 1. One-electron self-energy Feynman diagrams of second order in a...

In the subsequent discussion we shall need the irreducible 2- and 3-point functions i.e. the electron self energy Sy(p), the vacuum polarisation /7k,pv( ) and the full vertex function rv, PuP2% as knowledge of I vip) and determines the corresponding propagators Gy(p) and Dk,mv( ) completely and fy. iPuPz) represents the perturbative corrections to the free vertex The connection between these quantities is established by the Dyson equations (see e.g. [26])... 

Fermi, on investigating this same problem of the electrons self-energy, recognized that the divergences resulted from the point-like character of the charges (Schweber 2002). 

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