Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of $2^3P_J$ levels in helium are obtained by the calculation of contributions of order $\alpha^5 Ry$. New results for transition frequencies, $\nu_{01} = 29 616 943.01(17)$ kHz and $\nu_{12} = 2 291 161.13(30)$ kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.