Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Communications in Mathematical Physics |
Volume | 312 |
Issue number | 3 |
Pages (from-to) | 847-882 |
Number of pages | 36 |
ISSN | 0010-3616 |
DOIs | |
Publication status | Published - 2012 |
Links
- http://arxiv.org/abs/1105.0521
Accepted author manuscript
ID: 40301789