Relativistic Strong Scott Conjecture: A Short Proof

Creators: Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz

Abstract

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.

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.

Attached Files

Submitted - 2009.02474.pdf

Files

2009.02474.pdf

Files (165.8 kB)

Name	Size	Download all
2009.02474.pdf md5:4fa7bc5d82bd3300a17ae63f8ea2c918	165.8 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes