Second-Order Corrections to the Fine Structure of Helium. II. Contributions fromP1andD3Intermediate States

The contributions from the three spin-dependent Breit operators in second-order perturbation theory are calculated when the symmetries of the intermediate states are odd ${}_{}{}^1{}_{}{}^{}P$ or ${}_{}{}^3{}_{}{}^{}D$. Standard Hylleraas expansions with up to 165 terms are used for the perturbations of the wave functions. The large interval of the fine structure of the $2{}_{}{}^3{}_{}{}^{}P$ level in helium is increased by 2.17(2)×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ by ${}_{}{}^1{}_{}{}^{}P$, and by 0.0089(6)×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ by ${}_{}{}^3{}_{}{}^{}D$. Two methods for handling angular integration over $D$ tensors are described.