Doubly excited ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ resonant states in ${\mathrm{Ps}}^{\mathrm{-}}$ are calculated using a method of complex-coordinate rotation. Resonance parameters (both resonance positions and widths) for doubly excited states associated with the n=2, 3, 4, 5, and 6 thresholds of positronium atoms are evaluated using elaborate Hylleraas-type functions. In addition to ten Feshbach-type resonances lying below various Ps thresholds, we have identified three shape resonances, one each lying above the n=2, 4, and 6 Ps thresholds. It is further noted that the energy levels for the present ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ states are nearly degenerate with respect to the previously calculated ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ states. Such a symmetric character suggests that the highly and doubly excited ${\mathrm{Ps}}^{\mathrm{-}}$, similar to its counterpart in ${\mathrm{H}}^{\mathrm{-}}$, would exhibit rovibrational behaviors analogous to those of XYX triatomic molecules.

• Received 9 December 1991

DOI:https://doi.org/10.1103/PhysRevA.45.6268