Truncated dipole series in the electron-hydrogen and positron-hydrogen systems

Dipole series in H${}^{-}$ and in the positron-hydrogen system are studied in a coupled-channel calculation, in which the short-range part of the interaction between the electron or positron and the excited hydrogen core is modeled by a local potential, adjusted to reproduce low-lying states of the respective series. Consideration of the fine-structure splitting and radiative corrections enables us to describe the termination of the series towards the nondegenerate threshold. For the ${}^1{S}^e$ series below the $N=2\mathrm{}$ threshold we give quantitative predictions for the number of resonances and their energies.