Solutions of the Dirac-Fock equations without projector

Éric Paturel

Journées équations aux dérivées partielles (2000)

  • page 1-10
  • ISSN: 0752-0360

Abstract

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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 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 .

How to cite

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Paturel, 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 $N &lt;Z+1$ and $\alpha \max (Z, N) &lt;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 $N &lt;Z+1$ and $\alpha \max (Z, N) &lt;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

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  3. [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. [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. [5] I. P. Grant. Relativistic Calculation of Atomic Structures. Adv. Phys., 19:747-811, 1970. 
  6. [6] Y.K. Kim. Relativistic self-consistent field theory for closed-shell atoms. Phys. Rev., 154:17-39, 1967. 
  7. [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. [8] P.-L. Lions. Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys., 109 (1):33-97, 1987. Zbl0618.35111MR88e:35170
  9. [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. [10] B. Swirles. The relativistic self-consistent field. Proc. Roy. Soc., A 152:625-649, 1935. Zbl0013.13603JFM61.1574.02
  11. [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. [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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