Coulomb perturbation calculations in momentum space and application to quantum-electrodynamic hyperfine-structure corrections

Adaptation of the momentum-space Schr\"odinger-Coulomb Green's function for second-order perturbation calculations of the bound-state energy levels of hydrogenic atoms is demonstrated. The numerical viability of the formulas derived is proven by recalculating the contribution in second order of the spin-spin operator to the hydrogen hyperfine-structure residual R=(8ν2S-ν1S)ν1S. Application to positronium hyperfine structure is discussed.