Second-order contributions to the fine structure of helium from all intermediate states

For the theoretical assessment of the 2³P helium fine structure to become comparable to the precision measurements that have been made, it is necessary that the theory be calculated through order α⁶mc². In particular, the second-order contribution from the Breit and mass-polarization operators must be evaluated to an accuracy of 1% or so. In this work, for each of five possible intermediate state symmetries the Dalgarno-Lewis method is used to obtain the first-order perturbed wave function, from which the second-order energy follows by integration. Both the perturbed and unperturbed wave functions are expanded in Hylleraas-type series with a progressively larger number of terms, the second-order energies being computed at each stage; up to 455 terms are used for ³P intermediate states and up to 286 for ¹P, ³D, ¹D, and ³F. The sequence of second-order energy results for each symmetry is extrapolated to the limit of an infinite number of basis functions to arrive at a final result. The ³P, ¹P, and ³D states will contribute to both the larger and the smaller fine-structure intervals ν₀₁ and ν₁₂, respectively, while ³F and ¹D states affect only ν₁₂. The total theoretical result, up to order α⁶mc², for ν₀₁ is much more accurate than that for ν₁₂, allowing the fine-structure constant α to be determined very precisely by comparison of theory to experiment, with the result α^-1=137.03608(13), good to 0.94 ppm.