Speaker
Description
Bethe logarithm is a component of one of the leading quantum electrodynamic energy correction for atoms and molecules. This correction is of the order of $\alpha^{3}$.
A method for calculating the Bethe logarithm is presented. It is an alternative to the method of Schwartz \cite{Schwartz} which has been used in most of the atomic and molecular calculations. The present method was introduced in the paper by M Stanke et al. \cite{Stanke}. It is based on spectral decomposition of the operator that appears in the Bethe correction. In the present work we implement the method in calculations of bound electronic states of multi-electron atoms and two-centered molecules. A similar method is also used to calculate the adiabatic correction. All calculations presented here are done using an approach based on the Born-Oppenheimer approximation. The wave functions are expanded using all-electron explicitly correlated Gaussian functions with shifted centers. The problem of selecting appropriate basis sets for the spectral decomposition of the Bethe-logarithm operator is discussed. Tests are performed to find the most effective approach.
C. Schwartz, Phys. Rev. 123, 1700 (1961).
M. Stanke, L. Adamowicz, D. Kedziera, Mol. Phys. 111, 1-6 (2013).
