Bethe Logarithm and QED Shift for Lithium

A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 ²S_1/2 and excited 3 ²S_1/2 states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order α³ Ry. The calculated 3 ²S_1/2–2 ²S_1/2 transition frequency for ⁷Li is 27 206.092 6(9)  cm^-1, and the ionization potential for the 2 ²S_1/2 state is 43 487.158 3(6)  cm^-1. The ⁷Li–⁶Li isotope shift is also considered, and all the results compared with experiment.