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Relativistic Strong Scott Conjecture: A Short Proof

Frank, Rupert L. and Merz, Konstantin and Siedentop, Heinz (2020) Relativistic Strong Scott Conjecture: A Short Proof. . (Unpublished)

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We consider heavy neutral atoms of atomic number Z modeled with kinetic energy (c²p² + c⁴)^(1/2) − c² used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale Z⁻¹ in the limit Z,c → ∞ keeping Z/c fixed. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Additional Information:The authors warmly thank Barry Simon for his initial contributions and continuing support and interest in the relativistic strong Scott conjecture. They also acknowledge partial support by the U.S. National Science Foundation through grants DMS-1363432 and DMS-1954995 (R.L.F.), by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through grant SI 348/15-1 (H.S.) and through Germany’s Excellence Strategy EXC-2111 390814868 (R.L.F., H.S.). One of us (K.M.) would like to thank the organizers of the program Density Functionals for Many-Particle Systems: Mathematical Theory and Physical Applications of Effective Equations, which took place at the Institute for Mathematical Sciences (IMS) at the National University of Singapore (NUS), for their invitation to speak, their kind hospitality, as well as for generous financial support by the Julian Schwinger foundation that made his stay possible.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SI 348/15-1
Deutsche Forschungsgemeinschaft (DFG)EXC-2111 390814868
Julian Schwinger FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20211004-222648670
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111195
Deposited By: George Porter
Deposited On:04 Oct 2021 23:09
Last Modified:04 Oct 2021 23:09

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