We consider the zero mass limit of a relativistic Thomas-Fermi-Weizsäcker model of atoms and molecules. We find bounds for the critical nuclear charges that ensure stability.
REFERENCES
1.
Benguria
, R. D.
and Pérez-Oyarzún
, S.
, “The ultrarelativistic Thomas-Fermi-von Weizsäcker model
,” J. Phys. A
35
, 3409
–3414
(2002
).2.
Engel
, E.
and Dreizler
, R. M.
, “Field-theoretical Approach to a Relativistic Thomas-Fermi-Weizsäcker Model
,” Phys. Rev. A
35
, 3607
–3618
(1987
).3.
Engel
, E.
and Dreizler
, R. M.
, “Solution of the relativistic Thomas-Fermi-Dirac-Weizsäcker Model for the Case of Neutral Atoms and Positive Ions
,” Phys. Rev. A
38
, 3909
–3917
(1988
).4.
Frank
, R. L.
, Siedentop
, H.
, and Warzel
, S.
, “The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
,” Commun. Math. Phys.
(in press).5.
Hodges
, C. H.
, “Quantum Corrections to the Thomas-Fermi Approximation—The Kirzhnits Method
,” Can. J. Phys.
51
, 1428
–1437
(1973
).6.
Kirznits
, D. A.
, Field Theoretical Methods in Many Body Systems
(Pergamon
, New York
, 1967
).7.
Lieb
, E. H.
, “Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom without Electron Repulsion
,” Commun. Math. Phys.
85
, 15
–25
(1982
).8.
Lieb
, E. H.
, “Thomas-Fermi and Related Theories of Atoms and Molecules
,” Rev. Mod. Phys.
53
, 603
–641
(1981
).9.
Lieb
, E. H.
and Daubechies
, I.
, “One electron relativistic molecules with Coulomb interaction
,” Commun. Math. Phys.
90
, 497
–510
(1983
).10.
Lieb
, E. H.
, Loss
, M.
, and Siedentop
, H.
, “Stability of Relativistic Matter via Thomas-Fermi Theory
,” Helv. Phys. Acta
69
, 974
–984
(1996
).11.
Lieb
, E. H.
and Yau
, H.
, “Many-Body Stability Implies a Bound on the Fine-Structure Constant
,” Phys. Rev. Lett.
61
, 1695
–1697
(1988
).12.
Lieb
, E. H.
and Yau
, H.
, “The Stability and Instability of Relativistic Matter
,” Commun. Math. Phys.
118
, 177
–213
(1988
).13.
Tomishima
, Y.
and Yonei
, K.
, “Solution of the Thomas-Fermi-Dirac Equation with a Modified Weizsäcker Correction
,” J. Phys. Soc. Jpn.
21
, 142
–153
(1966
).14.
von Weizsäcker
, C. F.
, “Zur Theorie de Kernmassen
,” Z. Phys.
96
, 431
–458
(1935
).15.
Voronoi
, G.
, “Nouvelles applications des paramètres continus à la théorie des formes quadratiques
,” J. Reine Angew. Math.
133
, 97
–178
(1907
).© 2008 American Institute of Physics.
2008
American Institute of Physics
You do not currently have access to this content.
