Orderα4R∞corrections to the fine-structure splitting of positroniumPlevels

The order ${\mathrm{\alpha }}^4$ ${\mathit{R}}_{\mathrm{\infty }}$ corrections to the fine-structure splitting of positronium P levels are found. The calculation is reduced to the ordinary perturbation theory for the nonrelativistic Schrödinger equation. The perturbation operators have the Breit-type structure and are obtained by calculating on-mass-shell diagrams. The correction found is -0.64 MHz for the $2^3$ ${\mathit{P}}_{0\mathrm{-}}$ $2^1$ ${\mathit{P}}_1$ energy splitting.