Lamb Shift Excitation Energy in the Ground State of the Helium Atom

The evaluation of the Lamb shift excitation requires a knowledge of the oscillator strengths for transitions to all states which may be reached by dipole transitions from the ground state. The oscillator strengths for transitions to the continuum states ($1s, \epsilon p$) and ($2s, \epsilon p$) are calculated, using the 18-parameter ground-state wave function of Chandrasekhar and Herzberg. For the excited state in the continuum, a Hartree wave function is evaluated and used. It is shown that the error due to exchange and polarization in the $f$ value for high excitation energy $E$ of the $p$-state electron is only of relative order $\frac{1}{E}$, i.e., of absolute order of $E^{-\frac{9}{2}}$. The $f$ values for transitions to states other than ($1s, \epsilon p$) and ($2s, \epsilon p$) are also considered.