Geodesic
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction
Documenta mathematica, Tome 14 (2009), pp. 463-516
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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.
DOI : 10.4171/dm/279
Classification : 35Q40, 46N50, 47N50, 81V45, 81V55
Mots-clés : ground state energy, heavy atoms, relativistic Coulomb system, Scott correction, Brown-Ravenhall operator 
@article{10_4171_dm_279,
     author = {Rupert L. Frank and Heinz Siedentop and Simone Warzel},
     title = {The energy of heavy atoms according to {Brown} and {Ravenhall:} the {Scott} correction},
     journal = {Documenta mathematica},
     pages = {463--516},
     year = {2009},
     volume = {14},
     doi = {10.4171/dm/279},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/279/}
}
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Rupert L. Frank; Heinz Siedentop; Simone Warzel. The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Documenta mathematica, Tome 14 (2009), pp. 463-516. doi: 10.4171/dm/279

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