Many-body Breit interaction

Since the relativistic many-body Hamiltonian cannot be expressed in closed potential form, which means it is unbound, projection one- and two-electron operators are used to solve this problem [39], The operator projects onto the space spanned by the positive-energy spectrum of the Dirac-Fock-Coulomb (DFC) operator. In this form, the no-pair Hamiltonian [40] is restricted then to contributions from the positive-energy spectrum and puts Coulomb and Breit interactions on the same footing in the SCF calculations. 

For many types of electron spectroscopies there are still comparatively few studies of SOC effects in molecules in contrast to atoms, see, e.g., [1, 2, 3, 4, 5, 6, 7] and references therein. This can probably be referred to complexities in the molecular analysis due to the extra vibrational and rotational degrees of freedom, increased role of many-body interaction, interference and break-down effects in the spectra, but can also be referred to the more difficult nature of the spin-orbit coupling itself in polyatomic species. Modern ab initio formulations, as, e.g., spin-orbit response theory [8] reviewed here, have made such investigations possible using the full Breit-Pauli spin-orbit operator. 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

In the following sections we first present results from work done in collaboration with S.A. Blundell and W.R. Johnson [40]. The basic atomic physics part of this calculation has not been improved on in accuracy, but the treatment of the Breit interaction and radiative corrections has changed. As mentioned in the introduction, it would be highly desirable for a reader with more powerful many-body methods to repeat the calculation leading to Eq. 46, hopefully reducing the 1 percent error estimate to a few tenths of a percent. 

Table 9.4 Fine-structure splitting AE Pq — Pi of the magnesium-like ions Sc + and in cm 1. In addition, we have included results from an elaborate many-body perturbation theory (MBPT) study (including the Breit interaction) by Johnson and co-workers [504]. The experimental data have been taken from Refs. [505] and [506]. (See Refs. [506] and [504] for further references to the literature on Mg-like ions.)...

In the paragraphs below we review some of the recent progress on relativi tlc many-body calculations which provide partial answers to the first of these questions and we also describe work on the Brelt Interaction and QED corrections which addresses the second question. We begin in Section IT with a review of applications of the DF approximation to treat inner-shell problems, where correlation corrections are insignificant, but where the Breit Interaction and QED corrections are important. Next, we discuss, in Section III, the multiconfiguration Dirac-Fock (MCDF) approximation which is a many-body technique appropriate for treating correlation effects in outer shells. Finally, in Section IV, we turn to applications of the relativistic random-phase approximation (RRPA) to treat correlation effects, especially in systems involving continuum states. 

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