Doubly excited states of the positronium molecule

The projection method with explicitly correlated Gaussians is used to demonstrate the existence of two doubly excited states of the positronium molecule (Ps(2)). One is below the Ps(n = 2) + Ps(n = 2) threshold, with A(1) symmetry, and the other is below the Ps(n = 2) + Ps(n = 3) threshold, with E symmetry. These states exist as resonances in the Ps-Ps continuum. Moreover, the resonance positions and resonance widths of the two states are calculated using the complex rotation method with basis sets obtained via the orthogonalizing pseudoprojector method. The resonance positions obtained using the complex rotation method agree with the results of the orthogonalizing pseudoprojector method. We also investigate the various structural properties of these states as well as the decay probabilities of 2 gamma emission due to electron-positron annihilation.