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Solutions of the Dirac-Fock equations without projector

Éric Paturel — 2000

Journées équations aux dérivées partielles

In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with N electrons turning around a nucleus of atomic charge Z , satisfying N < Z + 1 and α max ( Z , N ) < 2 / ( 2 / π + π / 2 ) , where α is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on N .

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