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

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.

@article{JEDP_2000____A12_0,
     author = {Paturel, \'Eric},
     title = {Solutions of the {Dirac-Fock} equations without projector},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {12},
     publisher = {Universit\'e de Nantes},
     year = {2000},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2000____A12_0/}
}
TY  - JOUR
AU  - Paturel, Éric
TI  - Solutions of the Dirac-Fock equations without projector
JO  - Journées équations aux dérivées partielles
PY  - 2000
DA  - 2000///
PB  - Université de Nantes
UR  - http://www.numdam.org/item/JEDP_2000____A12_0/
LA  - en
ID  - JEDP_2000____A12_0
ER  - 
Paturel, Éric. Solutions of the Dirac-Fock equations without projector. Journées équations aux dérivées partielles (2000), article  no. 12, 10 p. http://www.numdam.org/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. | MR 99i:47091 | Zbl 0917.47057

[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. | MR 86b:58021 | Zbl 0559.58019

[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. | MR 2000j:81057 | Zbl 0938.35149

[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 56 #10566

[8] P.-L. Lions. Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys., 109 (1):33-97, 1987. | MR 88e:35170 | Zbl 0618.35111

[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 01591292

[10] B. Swirles. The relativistic self-consistent field. Proc. Roy. Soc., A 152:625-649, 1935. | JFM 61.1574.02 | Zbl 0013.13603

[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 98g:81036

[12] C. Tix. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc., 30(3):283-290, 1998. | MR 99b:81047 | Zbl 0939.35134