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 -