Bethe logarithm for the lithium atom from exponentially correlated Gaussian functions

Abstract

The calculation of Bethe logarithm for the ground state of the lithium atom is presented. The Bethe logarithm is the main QED effect coming from the electron self-interaction, which has not been obtained yet. Both results for the infinite nuclear mass, $\mathrm{ln}{k}_{0}=5.17817(3),$ and the mass polarization correction, $\ensuremath{\Delta}\mathrm{ln}{k}_{0}=0.114(3),$ significantly improve the hitherto theoretical values for the lithium ground-state energy. They allow from one side to test the theory against precise measurements of transition frequencies and from the other side, to improve the accuracy of determination of the difference in the square of nuclear charge radii from the isotope-shift measurements. The applied calculational method is based on the well adapted explicitly correlated Gaussian basis set and can be extended to other few-electron atoms and molecules.