Lowest order QED corrections for the H- and Mu- ions

Lowest order (∼α3) QED corrections ΔE(3) and ΔEM(3) are determined for the ground 11S(L=0)-states in the three-body negatively charged hydrogen and muonium ions, i.e. in the H-∼, T-, D-, 1H- and Mu-(=μ+e-e-) ions. The best-to-date non-relativistic variational wave functions (e.g., E(H-∼)=-0.5277510165443771965867 a.u.) have been used in our present calculations. In particular, for the ΔEM(3) correction which includes the nuclear recoil correction we have obtained ∼8207.191MHz for the T- ion, 8203.207 MHz for the D- ion, 8191.240 MHz for the 1H- ion and 8004.739 MHz for the Mu- ion. Also, the analytical regularization and numerical computations of some singular expectation values are considered in detail