Ground state energy of large atoms in a self-generated magnetic field

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Erdos, Laszlo
Solovej, Jan Philip
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Abstract
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We consider a large atom with nuclear charge $Z$ described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous $Z\to \infty$, $\al\to 0$ limit if $Z\al^2\leq \kappa$ for some universal $\kappa$, where $\al$ is the fine structure constant.
Keywords
Mathematical Physics, 81Q10
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