# On the maximal ionization for the atomic Pauli operator

Johnson, Tomas and Melgaard, Michael (2005) On the maximal ionization for the atomic Pauli operator. Proceedings of the Royal Society A, 461 (2063). pp. 3355-3364. ISSN 1471-2946

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## Abstract

Within the Born-Oppenheimer approximation Lieb proved that the
number of non-relativistic, spin-$\frac{1}{2}$ particles that
can be bound to an atom of nuclear charge $Z$ in the presence
of an external magnetic field satisfies $N_{\max} < 2Z+1$, provided the
magnetic field tends to zero at infinity and the coupling
between the magnetic field and the spin is ignored.
Assuming that the magnetic field is generic, we prove
an upper bound which holds when the spin-field coupling is
included; the set of generic magnetic fields contains an open,
dense subset of $[L^{3/2}(\R^{3})]^{3}$.

Item Type: Article Ionization; Pauli operator; magnetic Schrödinger operator; Hardy inequality School of Mathematical and Physical Sciences > Mathematics Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems Michael Melgaard 19 Sep 2013 11:34 19 Sep 2013 11:34 http://sro.sussex.ac.uk/id/eprint/46383