A two-dimensional pseudospectral Hartree-Fock method for low-Z atoms in intense magnetic fields

TL;DR

This paper introduces a pseudospectral Hartree-Fock computational method for calculating energy levels of low-Z atoms like helium and lithium in extremely strong magnetic fields, achieving accurate results efficiently without basis function assumptions.

Contribution

The study presents a novel two-dimensional pseudospectral Hartree-Fock method that is more computationally efficient and accurate for low-Z atoms in intense magnetic fields, avoiding traditional basis function assumptions.

Findings

Accurate energy levels for helium and lithium in magnetic fields up to 10^8-10^9 T.

Identification of two new lithium states not previously studied.

Method reduces computational time to seconds for helium-like systems.

Abstract

The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these two- and three-electron systems in a self-consistent manner. The method 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. It is seen that the results obtained here for a few of the most tightly bound states of each of the atoms, helium and lithium, are in good agreement with findings elsewhere. In this regard, we report new data for two new states of lithium that have not been studied thus far in the literature. It is also seen that the pseudospectral method employed here is considerably more economical, from a computational point of view, than previously employed methods such as a finite-element based approach. The key enabling advantage of the method described here is the short computational times which are on the order of seconds for obtaining accurate results for heliumlike systems.