High Precision Calculation of Fine Structure Splittings in Helium and He-Like Ions

Abstract

Fine structure splittings for the $1s2p$ ${}_{}{}^3{}_{}{}^{}P$ state of helium are calculated to a computational accuracy of 3 parts in ${10}^9$, including all terms up to $O\left({\alpha }^6{\mathrm{mc}}^2\right)$. The results differ notably from recent high precision measurements in He and ${\mathrm{Be}}^{2+}$, but there is good agreement for ${\mathrm{Li}}^{+}$, ${\mathrm{B}}^{3+}$, and ${\mathrm{F}}^{7+}$. A comparison with relativistic configuration interaction calculations [M H. Chen et al., Phys. Rev. A 47, 3692 (1993)] indicates close agreement for $Z\ge 10$, and lends strong support to both calculations.