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 $\mathrm{\text{Ps}}-\mathrm{\text{Ps}}$ 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.

中文翻译：

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正电子分子的双激发态

高斯显式相关的投影方法用于证明正电子分子（Ps${}_2$）。一个低于Ps$（ñ=2）$ $+$ 聚苯乙烯$（ñ=2）$ 阈值 ${\mathrm{一种}}_{\mathrm{1个}}$ 对称，另一个低于Ps$（ñ=2）$ + Ps $（n = 3）$阈值，其中 $Ë$对称。这些状态作为共振存在于$\mathrm{\text{聚苯乙烯}}-\mathrm{\text{聚苯乙烯}}$连续体。此外，使用复旋转法，以通过正交伪投影仪法获得的基集，计算两种状态的共振位置和共振宽度。使用复数旋转法获得的共振位置与正交伪投影仪法的结果一致。我们还研究了这些状态的各种结构特性以及2的衰减概率$\gamma$ 电子正电子an灭导致的发射。