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arXiv · 2411.12427

High-precision minmax solution of the two-center Dirac equation

Ossama Kullie
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Abstract

We present a high-precision solution of Dirac equation by numerically solving the minmax two-center Dirac equation with the finite element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or heavy atomic nuclear charge $Z$. A result is shown for the molecular ion ${\rm H}_2^+$ and the heavy quasi-molecular ion ${\rm Th}_2^{179+}$, with estimated fractional uncertainties of $\sim 10^{-23}$ and $\sim 10^{-21}$, respectively. The result of the minmax-FEM high-precision of the solution of the two-center Dirac equation, allows solid control over the required accuracy level and is promising for the application and extension of our method.

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Ossama Kullie. 2024-11-19. High-precision minmax solution of the two-center Dirac equation. https://doi.org/10.1103/physreva.110.052808

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