Geodesic
Solutions of the Dirac-Fock equations without projector
Journées équations aux dérivées partielles (2000), article no. 12, 10 p.

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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 αmax(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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Paturel, Éric. Solutions of the Dirac-Fock equations without projector. Journées équations aux dérivées partielles (2000), article  no. 12, 10 p. http://geodesic.mathdoc.fr/item/JEDP_2000____A12_0/

[1] V. I. Burenkov and W. D. Evans. On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms. Proc. Roy. Soc. Edinburgh Sect. A, 128 (5):993-1005, 1998. | Zbl | MR

[2] C. Conley and E. Zehnder. Morse-type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure Appl. Math., 37 (2):207-253, 1984. | Zbl | MR

[3] J. Desclaux. Relativistic Dirac-Fock expectation values for atoms with Z = 1 to Z = 120. Atomic Data and Nuclear Data Table, 12:311-406, 1973.

[4] M. J. Esteban and E. Séré. Solutions of the Dirac-Fock equations for atoms and molecules. Comm. Math. Phys., 203 (3):499-530, 1999. | Zbl | MR

[5] I. P. Grant. Relativistic Calculation of Atomic Structures. Adv. Phys., 19:747-811, 1970.

[6] Y.K. Kim. Relativistic self-consistent field theory for closed-shell atoms. Phys. Rev., 154:17-39, 1967.

[7] E.H. Lieb and B. Simon. The Hartree-Fock theory for Coulomb systems. Comm. Math. Phys., 53 (3):185-194, 1977. | MR

[8] P.-L. Lions. Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys., 109 (1):33-97, 1987. | Zbl | MR

[9] E. Paturel. Solutions of the Dirac-Fock equations without projector. Cahiers du Ceremade preprint 9954, mp_arc preprint 99-476, to appear in Annales Henri Poincaré (Birkhäuser). | Zbl

[10] B. Swirles. The relativistic self-consistent field. Proc. Roy. Soc., A 152:625-649, 1935. | Zbl | JFM

[11] C. Tix. Lower bound for the ground state energy of the no-pair Hamiltonian. Phys. Lett. B, 405(3-4):293-296, 1997. | MR

[12] C. Tix. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc., 30(3):283-290, 1998. | Zbl | MR