High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method

Abstract

The Dirac equation for H${}_2^{+}$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The ground-state relativistic energy is obtained with an accuracy of $10^{-20}$, which represents an improvement by several orders of magnitude, and is shown to be in good agreement with results obtained from perturbation theory.Highly accurate relativistic wavefunctions are obtained, which is a first step towards nonperturbative calculations of the one-loop self-energy correction in hydrogen molecular ions.

References in corpus (5)

• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Relativistic corrections of order mα^6 to the two-center problem
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Ro-vibrational spin-averaged transitions in the hydrogen molecular ions