Doubly excited autodissociating resonant states of positronium hydride

A doubly excited autodissociating resonant state in positronium hydride has been discovered, which is situated in a Rydberg series converging to the ${\mathrm{H}}^{\ensuremath{-}}(2{s}^{2})+{e}^{+}$ threshold. Previous research has noted a scarcity of such highly excited resonant states, particularly those with a doubly excited nature. The exploration of these states was made possible by employing a projection operator method supported by the stochastic variational method. Accurate calculations of the resonant positions and widths were performed using the complex coordinate rotation method with explicitly correlated Gaussians as basis functions. Our analysis has revealed the intrinsic structural characteristics of these highly excited states. The probability density distribution demonstrates that most resonant states of positronium hydride tend to favor either a ${\mathrm{H}}^{\ensuremath{-}}+{e}^{+}$ or ${\mathrm{Ps}}^{\ensuremath{-}}+{\mathrm{H}}^{+}$ configuration. However, two doubly excited resonant states exhibit a unique characteristic involving both the ${\mathrm{H}}^{\ensuremath{-}}+{e}^{+}$ and ${\mathrm{Ps}}^{\ensuremath{-}}+{\mathrm{H}}^{+}$ configurations. By integrating the probability density distribution with a quantum defect formula, highly excited resonances can be accurately assigned to either the ${\mathrm{H}}^{\ensuremath{-}}(2{s}^{2})+{e}^{+}$ or ${\mathrm{Ps}}^{\ensuremath{-}}(1{s}^{2})+{\mathrm{H}}^{+}$ Rydberg series, thereby reducing discrepancies compared to earlier classifications.

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