Five lowest ${}^{1}S$ states of the Be atom calculated with a finite-nuclear-mass approach and with relativistic and QED corrections

We have performed very accurate quantum mechanical calculations of the five lowest $S$ states of the beryllium atom. In the nonrelativistic part of the calculations we used the variational method and we explicitly included the nuclear motion in the Schrödinger equation. The nonrelativistic wave functions of the five states were expanded in terms of explicitly correlated Gaussian functions. These wave functions were used to calculate the leading ${\alpha }^2$ relativistic correction ($\alpha$ is the fine structure constant) and the ${\alpha }^3$ quantum electrodynamics (QED) correction. We also estimated the ${\alpha }^4$ QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement.