Abstract
A highly accurate calculation is supplemented by an adiabatic approximation to explore the resonance spectrum of positronium ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$. Surprisingly, the spectrum can be understood and classified with ${\mathrm{H}}_{2}^{+}$ quantum numbers by treating the interelectronic axis of ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ as an adiabatic parameter. We report and interpret the existence of $^{1}$S shape resonances, a phenomenon so far unknown in three-body Coulomb systems. The new results on ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ combined with previous results for ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ suggest the existence of a resonance spectrum and its similarity for all ABA Coulomb systems with charges \ensuremath{\Vert}${\mathit{Z}}_{\mathit{A}}$/${\mathit{Z}}_{\mathit{B}}$\ensuremath{\Vert}=1 and masses ${\mathit{m}}_{\mathit{A}}$/${\mathit{m}}_{\mathit{B}}$\ensuremath{\ge}1.
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