Relativistic and QED Corrections for the Beryllium Atom

Abstract

Complete relativistic and quantum electrodynamics corrections of order ${\alpha }^2$Ry and ${\alpha }^3$Ry 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 $\ln k_0(\mathrm{Be})=5.75034(3)$ and $\ln k_0({\mathrm{Be}}^{+})=5.75167(3)$ 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 $75192.514(80){\mathrm{cm}}^{-1}$ agrees with equally accurate available experimental values.