Precision calculation of fine structure in helium and Li ⁺

Abstract

The fine structure constant α can be extracted from high-precision spectroscopy of the 23PJ fine structure splittings in helium and light helium-like ions. In this work, the 23PJ 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 mα6 and 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.