High-angular-momentum $(L>~3)$ doubly excited resonance states of the positronium negative ion

We present a complex-coordinate rotation calculation of the doubly excited high-angular-momentum $(L>~3)$ resonance states of the positronium negative ion, ${\mathrm{Ps}}^{-},$ associated with the $N=3,$ $N=4\mathrm{}$, and $N=5\mathrm{}$ thresholds of the Ps atom. Products of Slater-type orbitals are used to represent the two-electron wave functions. For the Ps $N=5\mathrm{}$ threshold, states with angular momentum up to $L=8\mathrm{}$ are calculated. Results for doubly excited intrashell states are used to construct the supermultiplet structures of the energy levels of ${\mathrm{Ps}}^{-},$ revealing rotational and vibrational series similar to those for an XYX triatomic molecule.