Precision calculation of fine structure in helium and Li

The fine structure constant α can be extracted from high-precision spectroscopy of the 23 P J fine structure splittings in helium and light helium-like ions. In this work, the 23 P J fine structure splittings of helium and Li+ion are calculated,including relativistic and QED corrections of order mα4, mα4(m/M), mα5, mα5(m/M), and Douglas–Kroll operators of mα6and mα6(m/M), which provide an independent verification for the previous calculations performed by Drake [Can.J. Phys. 80 1195(2002)] and by Pachucki and Yerokhin [Phys. Rev. A 79 062516(2009); Phys. Rev. Lett. 104 070403(2010); Can. J. Phys. 89 1139(2011)]. The results of the three groups agree with each other.