The Breit equation

Breit eonstrueted a many-electron relativistic theory that takes into account such a retarded potential in an approximate way. Breit explicitly considered only the electrons of an atom, nucleus of which (similar to Dirac theory) created only an external field for the electrons. This ambitious project was only partly success- 

For two electrons the Breit equation has the form r 2 stands for the distance between electron 1 and electron 2) 

Gregory Breit (1899-1981), American physicist, professor St the universities New York, Wisconsin, Yale, Buffalo. Breit wHh Eugene Wigner introduced the resonance stales of particles, and with Condon creerfed the proton-proton scattering theory. 

The Breit Hamiltonian (in our example, for two electrons in an electromagnetic field) can be approximated by the following useful formula known as the Breit-Pauli Hamiltonian 

H = comes from the velocity dependence of mass, more pre- 

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A more accurate description is obtained by including other additional terms in the Hamiltonian. The first group of these additional terms represents the mutual magnetic interactions which are provided by the Breit equation. The second group of additional terms are known as effective interactions and represent, to second order perturbation treatment, interaction with distant configurations . These weak interactions will not be considered here. 

It is known that to the lowest order in aZ the relativistic recoil correction to the energy levels can be derived from the Breit equation. Such a derivation was made by Breit and Brown in 1948 [1] (see also [2]). They found that the relativistic recoil correction to the lowest order in aZ consists of two terms. The first term... 

We commented that the second term in (3.133) is incorrect, and gave for the orbit-orbit interaction the correct form in (3.145),but without justification. We now examine the interaction between electrons more careftilly, both to justify the earlier assumption and also to prepare the ground for our later discussion of the Breit equation. 

The first stage in deriving a molecular Hamiltonian is to reduce the Breit equation to non-relativistic form and Chraplyvy [17] has shown how this reduction can be performed by using an extension of the Foldy-Wouthuysen transformation. First let us remind ourselves of the most important features in the transformation of the Dirac Hamiltonian. The latter was written (see (3.57) and (3.58)) as... 

Derivation of nuclear spin interactions from the Breit equation... 

It is possible to obtain the nuclear spin magnetic interaction terms by starting from the Breit equation. We recall that the Breit Hamiltonian describes the interaction of two electrons of spin 1 /2, each of which may be separately represented by a Dirac Hamiltonian ... 

The formalism for treating light atom systems begins with the Breit equation. The atomic spin-orbit Hamiltonian is given by (5)... 

The reduction of the Breit equation into a four-component form of interest is a complicated, tedious and not fully exact process since the Breit operator itself is precise only to the order of 1/c2 (the reader should consult more specialised literature [3-6]). For this purpose it is convenient to consider even operators of the form... 

The Lorenz transformation requires some additional terms in the electron-electron interaction resulting in the Breit operator. The two-electron Breit Hamiltonian consists of the Dirac Hamiltonian for the individual electrons plus the Breit operator. The decoupling of the Breit equation to the upper-upper subspace of interest results in the appearance of several new Hamiltonian terms. 

Finally, the Breit equation has been given. The equation goes beyond the Dirac model by taking into account the retardation effects. The Breit-Pauli expression for the Breit Hamiltonian contains several easily interpretable physical effects. 

The Breit equation a) is invariant with respect to the Lorentz transformation b) takes into account the interaction of the magnetic moments of electrons resulting from their orbital motion c) neglects the interaction of the spin magnetic moments d) describes only a single particle. 

The Breit equation is invariant with respect to the Lorentz transformation, but only within an accuracy up to some small terms. 

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