Second-Order Corrections to the Fine Structure of Helium

The fine-structure constant can be determined to high accuracy from precise measurements of the fine structure of the 2³P level in helium. One of the necessary calculations is to compute the contributions from the six Breit operators and the mass-polarization operator in second-order perturbation theory. The eighteen spin-dependent perturbations from intermediate ³P states are calculated by solving an inhomogeneous Schr\"odinger equation for the perturbation of the wave function by the variational method. The second-order contributions are then given by a single integral. These corrections are calculated using standard Hylleraas expansions with up to 165 terms for the perturbed wave functions, resulting in contributions to the two fine-structure intervals of the order of 10^-4 cm^-1, but only four of the results are sufficiently accurate.