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

Abstract

Lowest order ( ∼ α 3 ) QED corrections Δ E ( 3 ) and Δ E M ( 3 ) are determined for the ground 1 1 S ( 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 − ∞ ) = − 0.52775 10165 44377 19658 67 a.u.) have been used in our present calculations. In particular, for the Δ E M ( 3 ) correction which includes the nuclear recoil correction we have obtained ≈ 8207.191 MHz 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 〈 r i j − n 〉 are considered in detail.