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Volume 353 - International Conference on Precision Physics and Fundamental Physical Constants (FFK2019) - Poster session
Algorithm for calculating Bethe logarithm and adiabatic correction for atoms and two-centered molecules
E. Palikot,* M. Stanke
*corresponding author
Full text: Not available
Abstract
Bethe logarithm is one of the leading quantum electrodynamics energy correction of the order of $\alpha^{3}$.
Method of calculating expectation value of it in alternative way to Schwartz [1] and effective algorithm for basis functions selection is presented. The theoretical base paper for the work was [2]. The method proposed by Stanke was extended for calculate multi-electron atoms and two-centered molecules and is based on the knowledge of expected values of some function operator and the spectral decomposition. Calculations was done in Born-Oppenheimer approximation using explicitly correlated Gaussian functions with shifted centers. In both cases, atomic and molecular, one of the main problems was the choice of the basis set.

[1] SCHWARTZ, Charles. Lamb shift in the helium atom. Physical Review, 1961, 123.5: 1700.
[2] STANKE, Monika; ADAMOWICZ, Ludwik; KEDZIERA, Dariusz. Selection of a Gaussian basis set for calculating the Bethe logarithm for the ground state of the hydrogen atom. Molecular Physics, 2013, 111.9-11: 1063-1068.
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