High-precision results are presented for calculations of the nonrelativistic energies, relativistic corrections, and quantum electrodynamic corrections for the $2{}^{2}S$, $2{}^{2}P$, and $3{}^{2}S$ states of Li and ${\mathrm{Be}}^{+}$, using nonrelativistic wave functions expressed in Hylleraas coordinates. Bethe logarithms are obtained for the states of ${\mathrm{Be}}^{+}$. Finite mass corrections are calculated with sufficient accuracy to extract the nuclear charge radius from measurements of the isotope shift for the $2{}^{2}S-2{}^{2}P$ and $2{}^{2}S-3{}^{2}S$ transitions. The calculated ionization potential for ${\mathrm{Be}}^{+}$ is $146882.923\pm 0.005{\mathrm{cm}}^{-1}$.

• Received 27 March 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.243002