TY - JOUR

T1 - Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field

AU - Erdös, Laszlo

AU - Fournais, Søren

AU - Solovej, Jan Philip

PY - 2012

Y1 - 2012

N2 - We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that $Z\al^2\le \kappa_0$ for a sufficiently small $\kappa_0$, where $\al$ denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, $\al\to 0$ such that $\kappa =Z\al^2$ is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.

AB - We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that $Z\al^2\le \kappa_0$ for a sufficiently small $\kappa_0$, where $\al$ denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, $\al\to 0$ such that $\kappa =Z\al^2$ is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.

U2 - 10.1007/s00220-012-1468-1

DO - 10.1007/s00220-012-1468-1

M3 - Journal article

VL - 312

SP - 847

EP - 882

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -