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

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 - 2012/6

Y1 - 2012/6

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 Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) 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 Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) 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

SN - 0010-3616

VL - 312

SP - 847

EP - 882

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -