Scott correction for large atoms and molecules in a self-generated magnetic field

L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics 312 (2012) 847–882.

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Abstract
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.
Publishing Year
Date Published
2012-06-01
Journal Title
Communications in Mathematical Physics
Volume
312
Issue
3
Page
847 - 882
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Erdös L, Fournais S, Solovej J. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 2012;312(3):847-882. doi:10.1007/s00220-012-1468-1
Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics, 312(3), 847–882. https://doi.org/10.1007/s00220-012-1468-1
Erdös, László, Søren Fournais, and Jan Solovej. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics 312, no. 3 (2012): 847–82. https://doi.org/10.1007/s00220-012-1468-1.
L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3, pp. 847–882, 2012.
Erdös L, Fournais S, Solovej J. 2012. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 312(3), 847–882.
Erdös, László, et al. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics, vol. 312, no. 3, Springer, 2012, pp. 847–82, doi:10.1007/s00220-012-1468-1.

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