Frequency-independent Breit interaction

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" ... 

Finally, we emphasize that it should also be remembered that the Coulomb and frequency-independent Breit interaction are only the lowest order descriptions of the electron-electron interaction. 

Electron-Electron Frequency-Independent Breit Interaction... 

E is the contribution resulting from the frequency-independent Breit interaction... 

Rgure 9.4 Effect of the frequency-independent Breit interaction on lsi/2 and 2 i/2 ra-diai functions for He- and Be-like cations as measured by the first radial moment (r) =... 

This expression can formally be evaluated without assuming any further simplification for the electron-electron interaction potential energy operator i.e., g i,j) is still defined by Eq. (8.69) as the sum of the Coulomb and frequency-independent Breit interactions. As in the case of the one-electron DKH transformation, g i,j) acts as an integral operator in momentum space and hence does not commute with any expression containing momentum operators such as Aj or R , for example. With the abbreviation gij = g i,j) the total two-electron interaction operator reads... 

The same discussion applies equally well for the Breit interaction. Only the four terms of the second line of Eq. (12.70) yield even operators for g i,j) = The corresponding two-component form of the free-particle Foldy-Wouthuysen-transformed frequency-independent Breit interaction Bq reads... 

Any electromagnetic perturbation of the set of N electrons in a molecule finally leads to sums of operators that may be classified according to the number of electronic coordinates involved as one- or two-electron operators. Of course, if an electron experiences a truly external field a one-electron operator will describe this interaction. If two electrons interact via retarded magnetic fields of the moving electrons as expressed in the frequency-independent Breit interaction and, hence, in the Breit-Pauli Hamiltonian, two-electron interaction operators arise. 

M. Reiher, J. Hinze. Self-consistent treatment of the frequency-independent Breit interaction in Dirac-Fock and MCSCF calculations of atomic structures. 1. Theoretical considerations. /. Phys. B At. Mol. Opt. Phys., 32 (1999) 5489-5505. 

M. Reiher, C. Kind. Self-consistent treatment of the frequency-independent Breit interaction in EHrac-Fock calculations... 

The nuclei are modeled as spheres of imiform proton-charge distribution Z is the nuclear charge. R (Bohr) is the radius of that nucleus and is related to the atomic mass, A (amu), by R= 2.2677 10 Adding the frequency-independent Breit interaction. 

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