Relativistic Electron Interactions

Vilkas, M.J., Ishikawa, Y. and Koc, K. (1998) Quadratically convergent multiconfiguration Dirac-Fock and multireference relativistic configuration-interaction calculations for many-electron systems. Physical Review E, 58, 5096-5110. 

Earlier we mentioned briefly that the electron spin is perfectly consistent with the non-relativistic four-component Levy-Leblond theory [44,45]. The EC type interaction does not manifest in Dirac or Levy-Leblond theory. We shall show that on reducing the four-component Levy-Leblond equation into a two-component form the EC contribution arises naturally. A non-relativistic electron in an electromagnetic radiation field is described by the Levy-Leblond equation given by... 

A fully relativistic extension of the scheme put forward in [12] has been introduced in [19], including the transverse electron-electron interaction (Breit +. .. ) and vacuum corrections. Restricting the discussion to the no-pair approximation [28] for simplicity, we here compare this perturbative approach to orbital-dependent Exc to the relativistic variant of the adiabatic connection formalism [29], demonstrating that the latter allows for a direct extraction of an RPA-like orbital-dependent functional for Exc- In addition, we provide some first numerical results for atomic Ec. 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

Van Vleck (80) illustrated how Eq. (73) can be identified in the energy expression of the two interacting electrons in a non-relativistic field-free framework. For such a system the contribution to the electron-electron interaction energy Ey comprises the Coulomb energy Jy and the exchange energy Ky,... 

Relativistic energy of electron-electron interaction in isospin basis... 

In a relativistic case let us consider for the same purposes two subshells of equivalent electrons ni /1 2j 2 2 - General expressions do not depend on the explicit form of a two-electron interaction, therefore we shall not specify the operator type. Here, non-diagonal matrix elements of two sorts occur N1N2 — Ni — 1 IV2 + 1 and N1N2 — Ni — 2 N2 + 2. In the first case we have... 

Next the results from the relativistic random-phase approximation (RRPA) and the many-body perturbation theory (MBPT), also shown in Table 5.1, will be discussed. Because both calculations include basically the same electron-electron interactions, rather good agreement exists, and it is sufficient to concentrate only on the RRPA model. 

The results of a spin-polarization measurement of xenon photoelectrons with 5p5 2P3/2 and 5p5 2P1/2 final ionic states are shown in Fig. 5.21 together with the results of theoretical predictions. Firstly, there is good agreement between the experimental data (points with error bars) and the theoretical results (solid and dashed curves, obtained in the relativistic and non-relativistic random-phase approximations, respectively). This implies that relativistic effects are small and electron-electron interactions are well accounted for. (In this context note that the fine-structure splitting in the final ionic states has also to be considered in... 

A last possibility to produce relativistic electrons in the cluster atmospheres is due to the interaction of high-E gamma-rays with low energy (CMB/IR) photons, with the subsequent production of e pairs (Timokhin et al. 2003). The main uncertainty of this last model is the unknown origin of the very high-E gamma-rays in clusters. 

The advent of relativistic electron beams generated from laser-plasma interactions opens the possibility of producing X-rays in the keV to 100 keV... 

The energy, Eth, of the X-rays produced depends on the interaction angle between the laser and the relativistic electron beam, electron beam direction, 9. It is given by [18] as... 

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