Geodesic
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction
Documenta mathematica, Tome 14 (2009), pp. 463-516.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider relativistic many-particle operators which -- according to Brown and Ravenhall -- describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas-Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev-Ga­gliar­do-Nirenberg-type inequality is established for the critical atomic Brown-Ravenhall operator. Moreover, we prove sharp upper and lower bounds on the eigenvalues of the hydrogenic Brown-Ravenhall operator up to and including the critical coupling constant.
Classification : 81V45, 81V55, 35Q40, 46N50, 47N50
Keywords: heavy atoms, ground state energy, relativistic Coulomb system, Scott correction, Brown-Ravenhall operator 
@article{DOCMA_2009__14__a11,
     author = {Frank, Rupert L. and Siedentop, Heinz and Warzel, Simone},
     title = {The energy of heavy atoms according to {Brown} and {Ravenhall:} the {Scott} correction},
     journal = {Documenta mathematica},
     pages = {463--516},
     publisher = {mathdoc},
     volume = {14},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a11/}
}
TY  - JOUR
AU  - Frank, Rupert L.
AU  - Siedentop, Heinz
AU  - Warzel, Simone
TI  - The energy of heavy atoms according to Brown and Ravenhall: the Scott correction
JO  - Documenta mathematica
PY  - 2009
SP  - 463
EP  - 516
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a11/
LA  - en
ID  - DOCMA_2009__14__a11
ER  - 
%0 Journal Article
%A Frank, Rupert L.
%A Siedentop, Heinz
%A Warzel, Simone
%T The energy of heavy atoms according to Brown and Ravenhall: the Scott correction
%J Documenta mathematica
%D 2009
%P 463-516
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a11/
%G en
%F DOCMA_2009__14__a11
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone. The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Documenta mathematica, Tome 14 (2009), pp. 463-516. http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a11/