Fermi-Breit interaction

Here frs and (ri-l tM> are, respectively, elements of one-electron Dirac-Fock and antisymmetrized two-electron Coulomb-Breit interaction matrices over Dirac four-component spinors. The effect of the projection operators is now taken over by the normal ordering, denoted by the curly braces in (15), which requires annihilation operators to be moved to the right of creation operators as if all anticommutation relations vanish. The Fermi level is set at the top of the highest occupied positive-energy state, and the negative-energy states are ignored. 

The fine structure was calculated by Pirenne [110] and independently by Berestetski [4J. Minor errors are corrected, and numerical results are given by Ferrell [45]. The approach used by these authors is to write down the Dirac equations for the two particles, and the interaction terms as they are expressed in quantum field theory. The equations can be transformed so that the particle spins appear explicitly. The interaction terms are found to comprise the Coulomb energy, the Breit interaction, and a term analogous to the Fermi expression for... 

The effect of the Breit interaction on the wave function can be conveniently studied by comparing radial moments (r) of shells calculated with Dirac-Coulomb and Dirac-Coulomb-Breit Hamiltonians. The effect is not very large as can be seen for Li- and Be-like ions in Figure 9.4. From the plot we note that the effect of the Breit interaction on the radial functions is small, but increases linearly with the nuclear charge number Z. Moreover, the four different models to describe the positive nuclear charge distribution (point-like, exponential, Gaussian shaped and Fermi) can hardly be distinguished. 

In lowest-order perturbation theory, the QED potential arises from one-photon exchange. This potential contains a static part (i.e. a velocity independent part), which is the Coulomb potential, and non-static corrections. These non-static terms are most commonly treated in the Fermi-Breit approximation, which gives the corrections to order w /c. The Fermi-Breit terms include a spin-spin interaction, a spin-orbit interaction, and a tensor interaction. They also include a spin-independent part which depends on the particle momenta. 

AE all-electron HF Hartree-Fock DHF DIrac-Hartree-Fock DC DIrac-Coulomb-Hamlltonlan +B Breit interaction in quasi-degenerate perturbation theory +QED quantum electrodynamic corrections (vacuum polarisation, self-energy) p.n. point nucleus f.n. finite (Fermi) nucleus exp. experimental data. 

The relativistic correction to the fermion kinetic energy is represented as a potential. The Breit-Fermi interaction includes the effects of transverse photon exchange as well as relativistic corrections to Coulomb photon exchange. The potentials are given with the assumption that the states acted on are S states with total spin 1. 

The terms 7 2, 3, H4 (crucial for the NMR experiment) correspond to the magnetic dipole-dipole interaction involving nuclear spins (the term H5 of the Breit Hamiltonian) the classical electronic spin - nuclear spin interaction (7 2) plus the corresponding Fermi contact term (Tia) and the classical interaction of the nuclear spin magnetic dipoles... 

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