Evaluation of the Bethe logarithm: from atom to chemical reaction

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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Cited by in corpus (10)

• Leading-order QED effects in the ground electronic state of molecular hydrogen
• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• Atomic Bethe logarithm in the mean-field approximation
• QED corrections to the correlated relativistic energy: one-photon processes
• Rovibrational computations for He${}_2^{+}$ X ${\Sigma }_{\mathrm{u}}^{+}$ including non-adiabatic, relativistic and QED corrections
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections