# Ground state solutions to Hartree–Fock equations with magnetic fields

Argaez, C and Melgaard, M (2017) Ground state solutions to Hartree–Fock equations with magnetic fields. Applicable Analysis. ISSN 0003-6811

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## Abstract

Within the Hartree-Fock theory of atoms and molecules we prove existence of a ground state in the presence of an external magnetic field when: (1) the diamagnetic effect is taken into account; (2) both the diamagnetic effect and the Zeeman effect are taken into account. For both cases the ground state exists provided the total charge $Z_{\rm tot}$ of the nuclei $K$ exceeds $N-1$, where $N$ is the number of electrons. For the first case, the Schr\"{o}dinger case, we complement prior results by allowing a wide class of magnetic potentials. In the second case, the Pauli case, we include the magnetic field energy in order to obtain a stable problem and we assume $Z_{\rm tot} \a^{2} \leq 0.041$, where $\a$ is the fine structure constant.

Item Type: Article School of Mathematical and Physical Sciences > Mathematics Analysis and Partial Differential Equations Research Group Michael Melgaard 14 Sep 2017 08:35 12 Dec 2017 13:42 http://sro.sussex.ac.uk/id/eprint/70192

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