Po1,3resonance states in positronium ions

Doubly excited ${}_{}{}^{1,3}{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ autodetaching resonances in ${\mathrm{Ps}}^{\mathrm{-}}$ have been calculated using the complex-rotation method, which has the advantage of giving resonance position and width at the same time. The wave function is of the Hylleraas type with number of terms up to 1330. Feshbach resonances associated with the positronium n=4, 5, and 6 thresholds are reported. In addition, we have also identified ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ shape resonances associated with the positronium n=4 and 6 thresholds, and a ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ shape resonance associated with the n=5 positronium threshold.