Erlangen 2022 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 44: Precision spectroscopy of atoms and ions (joint session A/Q)
Q 44.1: Poster
Wednesday, March 16, 2022, 16:30–18:30, P
Precise solution of the two-center Dirac equation using a finite-element-technique — •Ossama Kullie1, Stephan Schiller2, and Vladimir I. Koborov3 — 1Theoretical Physics, Institute of Physics, University of Kassel — 2Institut für Experimentalphysik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany — 3Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
In the field of spectroscopy of the molecular hydrogen ions H2+, HD+ etc., precise experimental transition frequencies are compared with ab initio predictions [3]. The solution of the two-center Dirac problem, one electron in the field of two fixed nuclei at distance R, is therefore of interest. Here, R≃2 Bohr. The numerical solution of the problem utilizes the finite-element method (FEM) [1,2]. Our technique allows determining the relativistic contribution to various rovibrational transition frequencies with spectroscopic accuracy. Our results are compared with perturbation theory based on the nonrelativistic one-body variational solution. The deviations found are smaller than the theory uncertainty stemming from uncalculated quantum-electrodynamic effects, and are therefore not resolvable experimentally. [1] O. Kullie et al, Chemical Physics Letters 383 (2004) 215-221. [2] O. Kullie, S. Schiller and V. I. Koborov, in preparation. [3] S. Alighanbari et al, Nature 581, 152 -158 (2020).