Speaker
Description
The largest source of uncertainty in the theory of spin-averaged rovibrational transitions in hydrogen molecular ions arises from uncalculated higher-order ($m\alpha^{8+}$) corrections to the one-loop self-energy [1]. These terms are extremely challenging to evaluate via the standard $Z\alpha$ expansion, therefore—similarly to the case of the hydrogen atom [2]—a numerical all-order approach is desirable. It was recently demonstrated that Gaussian basis sets are suitable for the evaluation of the self-energy for hydrogenlike ions [3], which is a significant step towards molecular calculations. In this contribution I will present a method for the high-precision solution of the Dirac equation in the Coulomb field of the two nuclei using a Gaussian basis set [4], and show that the necessary ingredients to the evaluation of the self-energy via the many-potential expansion can be readily obtained in this framework for the molecular case. The challenges that arise for low nuclear charges in the many-potential expansion approach will also be addressed.
[1] V. I. Korobov and J-Ph. Karr, Phys. Rev. A 104, 032806 (2021).
[2] U. Jentschura, P. J. Mohr, and G. Soff, Phys. Rev. Lett. 82, 53 (1999).
[3] D. Ferenc, M. Salman, and T. Saue, Phys. Rev. A 111, L040802 (2025).
[4] D. Ferenc and T. Saue, in preparation (2026).