Annihilation, bound state properties and photodetachment of the positronium negatively charged ion

Bound state properties of the negatively charged Ps$^{-}$ ion (or $e^{-} e^{+} e^{-}$) are discussed. The expectation values of operators which correspond to these properties have been determined with the use of the highly accurate wave functions constructed for this ion. Our best variational energy obtained for the Ps$^{-}$ ion is $E$ = -0.2620050 7023298 0107770 40051 $a.u.$ Annihilation of the electron-positron pair(s) in the negatively charged Ps$^{-}$ ion (or $e^{-} e^{+} e^{-}$) is considered in detail. By using accurate values for a number annihilation rates $\Gamma_{n \gamma}$, where $n$ = 1, 2, 3, 4 and 5, we evaluated the half-life $\tau_a$ of the Ps$^{-}$ ion against positron annihilation ($\tau_a = \frac{1}{\Gamma} \approx 4.793584140 \cdot 10^{-10}$ $sec$). Photodetachment of the Ps$^{-}$ ion is considered in the long-range, asymptotic approximation. The overall accuracy of our photodetachment cross-section of the Ps$^{-}$ ion is very good for such a simple approximation.