Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique

• URL: http://arxiv.org/abs/2204.07087v2
• Date: Wed, 4 May 2022 08:56:06 GMT
• Title: Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
• Authors: O. Kullie and S. Schiller
• Abstract summary: We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The computed total energies have estimated fractional uncertainties of a few times $10-20$ for unit charges and a bond length of 2 atomic units. The result is relevant for future precision experiments, whereas at present the uncertainties arising from the quantum electrodynamic treatment of the rovibrational transition frequencies are dominant.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues, systems that are an active experimental topic. The computation utilizes the 2-spinor minmax approach and the finite-element method. The computed total energies have estimated fractional uncertainties of a few times $10^{-20}$ for unit charges and a bond length of 2 atomic units. The fractional uncertainty of the purely relativistic contribution is $1\times10^{-17}$. The result is relevant for future precision experiments, whereas at present the uncertainties arising from the quantum electrodynamic treatment of the rovibrational transition frequencies. are dominant.

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