Abstract
We present recent progress in the calculation of the helium fine-structure splitting of the 23PJ states, based on the quantum electrodynamic theory. Apart from the complete evaluation of mα7 and m2/Mα6 corrections, we have performed extensive tests by comparison with all experimental results for light helium-like ions and with the known large nuclear charge asymptotics of individual corrections. Our theoretical predictions are still limited by the unknown mα8 term, which is conservatively estimated to be 1.7 kHz. However, comparison with the latest experimental result for the 23 P0 – 23 P2 transition [M. Smiciklas and T. Shiner, Phys. Rev. Lett. 105, 123001 (2010)] suggests that the higher-order contribution is in fact much smaller than the theoretical estimate. This means that the spectroscopic determination of a can be significantly improved if another measurement of the 23P0 – 23P2 transition in helium-like Li+ or Be2+ ion is performed.
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