Erdös, Laszlo^{2}; Fournais, Søren^{4}; Solovej, Jan Philip^{3}

Affiliations:

^{1} Department of Mathematics, Science and Technology, Aarhus University^{2} LMU Munchen^{3} Institut for Matematiske Fag, Københavns Universitet^{4} Department of Mathematics, Science and Technology, Aarhus University

DOI:

10.1063/1.3697417

Abstract:

We consider a large neutral molecule with total nuclear charge $Z$ in a model with self-generated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that $Z \alpha < 2/\pi$, where $\alpha$ denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit $Z \rightarrow \infty$, $\alpha \rightarrow 0$ such that $\kappa=Z \alpha$ is fixed. The leading term in the energy asymptotics is independent of $\kappa$, it is given by the Thomas-Fermi energy of order $Z^{7/3}$ and it is unchanged by including the self-generated magnetic field. We prove the first correction term to this energy, the so-called Scott correction of the form $S(\alpha Z) Z^2$. The current paper extends the result of \cite{SSS} on the Scott correction for relativistic molecules to include a self-generated magnetic field. Furthermore, we show that the corresponding Scott correction function $S$, first identified in \cite{SSS}, is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.

Type:

Journal article

Language:

English

Published in:

Journal of Mathematical Physics, 2012, Vol 53, Issue 9