Progress in helium fine-structure calculations and the fine-structure constant

The long-term goal of this work is to determine the fine-structure constant alpha from a comparison between theory and experiment for the fine-structure splittings of the helium 1s2p P-3(J) states. All known terms of order alpha(5) a.u. (alpha(7) mc(2)) arising from the electron-electron interaction, and recoil corrections of order alpha(4) mu/M a.u. are evaluated and added to previous tabulation. The predicted energy splittings are nu(0,1) = 29 616.946 42(18) MHz and nu(1,2) = 2291.154 62(31) MHz. Although the computational uncertainty is much less than +/-1 kHz, there is an unexplained discrepancy between theory and experiment of 19.4(1.4) kHz for nu(1,2).