High precision calculation of fine structure splittings in helium and He-like ions.

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