Lamb Shift in the Helium Atom

The calculation, first attempted by Kabir and Salpeter, of the mean excitation energy entering in the Lamb shift of the helium ground state is redone by a quite different approach. Our answer, $\ln \left[\frac{k_0}{r_y}\right]=4.370\mathrm{}\pm 0.004$, leaves theory and experiment on the ionization energy of helium in agreement within the experimental uncertainty of ±0.15 ${\mathrm{cm}}^{-1\mathrm{}}$. Incidental results are given for the electrostatic polarizability of He and ${\mathrm{H}}^{-}$ ground states and there is appended a new discussion of the construction of higher angular momentum eigenfunctions for the three-body problem.