Breit interaction, relativistic effects

Breit interaction, relativistic effects, 210 Brillouins theorem, 104 Brownian dynamics, 389 Broyden-Fletcher-Goldfarb-Shanno (BFGS) update in optimizations, 321 Brueckner theory, 138 Buckingham potential, 19... 

Note that the subscript on the a matrices refers to the particle, and a here includes all of the tlx, tty and components in eq. (8.4). The first correction term in the square brackets is called the Gaunt interaction, and the whole term in the square brackets is the Breit interaction. The Dirac matiices appear since they represent the velocity operators in a relativistic description. The Gaunt term is a magnetic interaction (spin) while the other term represents a retardation effect. Eq. (8.27) is more often written in the form... 

The plan of this paper is as follows - In section 2, the basic experimental data required in the re-evaluation of the empirical correlation energies of the N2 CO, BF and NO molecules are collected. The essential theoretical ingredients of our re-determination are given in section 3 including new fully relativistic calculations including the frequency independent Breit interaction and electron correlation effects described by second order diagrammatic perturbation theory for the Be-like ions B", C, O" ... 

SO coupling is a relativistic effect. The theory of the interaction of the magnetic moments of the electron spin and the orbital motion in one- and two-electron atoms has been formulated independently by Heisenberg and Pauli [12,13], shortly before the advent of the four-component Dirac theory of the electron [14]. Breit later has added the retardation correction [15]. The resulting Breit-Pauli SO operator, which can more elegantly be derived from the Dirac equation via a Foldy-Wouthuysen transformation [16], was thus well known for atoms since the early 1930s [17]. 

Judd, Crosswhite, and Crosswhite (10) added relativistic effects to the scheme by considering the Breit operator and thereby produced effective spin-spin and spin-other-orbit interaction Hamiltonians. The reduced matrix elements may be expressed as a linear combination of the Marvin integrals,... 

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. 

Quantum electrod)mamic (QED) effects are known to be very important for inner-shells, for example, in accurate calculations of X-ray spectra [61]. For highly charged few electron atoms they were found to be of similar size as the Breit correction to the electron-electron interaction [62]. Similar effects were also found for valence ns electrons of neutral alkali-metal and coinage metal atoms [63]. They are of the order of 1-2% of the kinetic relativistic effects there. The result for the valence ns electron is a destabilization, while for (n-l)d electron is an indirect stabilization. In the middle range (Z = 30-80) both the valence-shell Breit and the Lamb-shift terms behave similarly to the kinetic... 

Although this does not enter into the discussion of correlation effects, we point out the role of higher-order relativistic effects, such as the Breit interaction, on the spin-orbit splitting, which are not explicitly included. For the neutral Pb atom, the Breit interaction estimated by a four-component all-electron calculation using first order perturbation theory lowers the SCF spin-orbit splitting by 166 cm thus compensating partially the increase due to core-core and core-valence interactions [60]. 

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