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Solutions of the Dirac-Fock equations without projector. (English) Zbl 1072.81523

Summary: 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 \(\alpha\max(Z, N)\)<\({2\over {2\over \Pi}+{\Pi\over 2}}\), where \(\alpha \approx {1\over 137}\) is the fundamental constant of the electromagnetic interaction. This work is an improvement of an article of Esteban-Séré [M. J. Esteban and É. Séré, Commun. Math. Phys. 203, No. 3, 499–530 (1999; Zbl 0938.35149)], where the same result was proved under more restrictive assumptions on \(N\).

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q40 PDEs in connection with quantum mechanics
81V45 Atomic physics

Citations:

Zbl 0938.35149
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