 05428 Matthias Huber, Heinz Siedentop
 Solutions of the DiracFock Equations and the Energy of the ElectronPositron Field
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Dec 20, 05

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Abstract. We consider atoms with closed shells, i.e., the electron number $N$
is $2,\ 8,\ 10,...$, and weak electronelectron interaction. Then
there exists a unique solution $\gamma$ of the DiracFock equations
$[D_{g,\alpha}^{(\gamma)},\gamma]=0$ with the additional property
that $\gamma$ is the orthogonal projector onto the first $N$
positive eigenvalues of the DiracFock operator
$D_{g,\alpha}^{(\gamma)}$. Moreover, $\gamma$ minimizes the energy
of the relativistic electronpositron field in HartreeFock
approximation, if the splitting of $\gH:=L^2(\rz^3)\otimes \cz^4$ into
electron and positron subspace, is chosen selfconsistently, i.e.,
the projection onto the electronsubspace is given by the positive
spectral projection of $D_{g,\alpha}^{(\gamma)}$. For fixed
electronnucleus coupling constant $g:=\alpha Z$ we give
quantitative estimates on the maximal value of the fine structure
constant $\alpha$ for which the existence can be guaranteed.
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