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

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 ${\mathrm{H}}_2^{+}$ and the heavy quasi-molecular ion ${\mathrm{Th}}_2^{179+}$, 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.

References in corpus (4)

• Relativistic calculations of the ground state energies and the critical distances for one-electron homonuclear quasi-molecules
• Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
• High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion
• Ab initio QED calculations in diatomic quasimolecules