Two-center Dirac equation in a Gaussian basis set

Abstract:A method for solving the two-center Dirac equation using a Gaussian-product basis set tailored to the axial symmetry of diatomic systems is presented. For the ground state of H$_2^+$ at an internuclear distance $R=2.0~a_0$, we obtain a relativistic energy with relative precision at the $10^{-18}$ level. The properties of the basis set allow for an analytic Fourier transform of the wave function. As a first application we evaluate, for the first time, the zero-potential contribution to the one-loop self-energy for H$_2^+$ in Feynman and Coulomb gauges. Although this contribution is not separately gauge invariant, its calculation provides a proof of principle for the use of the present framework in prospective QED calculations.

arXiv:2610.03217 [quant-ph]

(or arXiv:2610.03217v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03217 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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