Evaluation of the Bethe logarithm: from atom to chemical reaction

• URL: http://arxiv.org/abs/2208.03033v3
• Date: Sun, 8 Jan 2023 10:19:57 GMT
• Title: Evaluation of the Bethe logarithm: from atom to chemical reaction
• Authors: D\'avid Ferenc and Edit M\'atyus
• Abstract summary: General computational scheme for the (non-relativistic) Bethe logarithm is developed. Implementation relies on Schwartz' method and minimization of a Hylleraas functional.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A general computational scheme for the (non-relativistic) Bethe logarithm is developed opening the route to `routine' evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small polyatomic and polyelectronic molecular systems. The implementation relies on Schwartz' method and minimization of a Hylleraas functional. In relation with electronically excited states, a projection technique is considered, which ensures positive definiteness of the functional over the entire parameter (photon momentum) range. Using this implementation, the Bethe logarithm is converged to a relative precision better than 1:10$^3$ for selected electronic states of the two-electron H$_2$ and H$_3^+$, and the three-electron He$_2^+$ and H+H$_2$ molecular systems. The present work focuses at nuclear configurations near the local minimum of the potential energy surface, but the computations can be repeated also for other structures.

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