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, ) and (2s, ) 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 1E, i. e. , of absolute order of E^-9{2}. The f values for transitions to states other than (1s, ) and (2s, ) are also considered. An accurate value of the average excitation energy is obtained by combining these results with a method previously used by Pekeris. The value obtained by this method is 80. 560. 90 ry, where the limits represent an estimate of the probable error. The corrections of order ^4 ry to the ionization energy are estimated roughly and are found to be -0. 0250. 01 cm^-1. When they are added to the radiative corrections of order ^3 ry evaluated by Kabir, Salpeter, Sucher, Dalgarno, and Stewart, the value of the Lamb shift becomes -1. 3610. 021 cm^-1, where the error is mainly due to the uncertainties in the estimate of corrections of order ^4 ry and the value of the average excitation energy. With this value of the Lamb shift correction, the theoretical ionization energy becomes 198310. 665 cm^-1, compared with Herzberg's experimental value of 198310. 80. 15 cm^-1.