# Solutions of the Dirac-Fock equations without projector

Journées équations aux dérivées partielles (2000)

- page 1-10
- ISSN: 0752-0360

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topPaturel, Éric. "Solutions of the Dirac-Fock equations without projector." Journées équations aux dérivées partielles (2000): 1-10. <http://eudml.org/doc/93389>.

@article{Paturel2000,

abstract = {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/(2/\pi + \pi /2) $, where $\alpha $ 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 $N$.},

author = {Paturel, Éric},

journal = {Journées équations aux dérivées partielles},

keywords = { electrons},

language = {eng},

pages = {1-10},

publisher = {Université de Nantes},

title = {Solutions of the Dirac-Fock equations without projector},

url = {http://eudml.org/doc/93389},

year = {2000},

}

TY - JOUR

AU - Paturel, Éric

TI - Solutions of the Dirac-Fock equations without projector

JO - Journées équations aux dérivées partielles

PY - 2000

PB - Université de Nantes

SP - 1

EP - 10

AB - 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/(2/\pi + \pi /2) $, where $\alpha $ 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 $N$.

LA - eng

KW - electrons

UR - http://eudml.org/doc/93389

ER -

## References

top- [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. Zbl0917.47057MR99i:47091
- [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. Zbl0559.58019MR86b:58021
- [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. Zbl0938.35149MR2000j:81057
- [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. MR56 #10566
- [8] P.-L. Lions. Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys., 109 (1):33-97, 1987. Zbl0618.35111MR88e:35170
- [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). Zbl1072.81523
- [10] B. Swirles. The relativistic self-consistent field. Proc. Roy. Soc., A 152:625-649, 1935. Zbl0013.13603JFM61.1574.02
- [11] C. Tix. Lower bound for the ground state energy of the no-pair Hamiltonian. Phys. Lett. B, 405(3-4):293-296, 1997. MR98g:81036
- [12] C. Tix. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc., 30(3):283-290, 1998. Zbl0939.35134MR99b:81047

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