Complete relativistic and quantum electrodynamics corrections of order α²Ry and α³Ry are calculated for the ground state of the beryllium atom and its positive ion. A basis set of correlated Gaussian functions is used, with exponents optimized against nonrelativistic binding energies. The results for Bethe logarithms lnk₀(Be)=5.750 34(3) and lnk₀(Be⁺)=5.751 67(3) demonstrate the availability of high precision theoretical predictions for energy levels of the beryllium atom and light ions. Our recommended value of the ionization potential 75 192.514(80) cm^-1 agrees with equally accurate available experimental values.
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Pachucki et al. (2004) studied this question.
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