Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field |
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Authors: | Email author" target="_blank">László?Erd?sEmail author S?ren?Fournais Jan?Philip?Solovej |
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Institution: | 1.Institute of Mathematics,University of Munich,Munich,Germany;2.Department of Mathematical Sciences,Aarhus University,Aarhus,Denmark;3.Department of Mathematics,University of Copenhagen,Copenhagen,Denmark |
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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 Z α 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 = Z α 2 is fixed, the ground state energy of the system is given by a two term expansion c 1 Z 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. |
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