Hydrogen and Helium atoms in strong magnetic fields

TL;DR

This paper presents a novel computational method for accurately calculating energy levels of hydrogen and helium atoms in strong magnetic fields, improving upon previous estimates and applicable to more complex systems.

Contribution

The study introduces a self-consistent two-dimensional Hartree-Fock approach that does not rely on basis functions or adiabatic approximations, enhancing accuracy for atomic structures in magnetic fields.

Findings

Improved estimates of low-lying energy states for hydrogen and helium.

Method applicable to atoms with more than two electrons.

No reliance on basis functions or adiabatic approximation.

Abstract

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.