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

Adaptation of the momentum-space Schrödinger-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 $R=\frac{(8\mathrm{}{\nu }_{2S}-{\nu }_{1S})}{{\nu }_{1S}}$. Application to positronium hyperfine structure is discussed.