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

TL;DR

This paper investigates the bound state properties, annihilation rates, and photodetachment cross-section of the negatively charged positronium ion (Ps$^{-}$), providing highly accurate calculations and new insights into its stability and interactions.

Contribution

The study presents highly accurate variational calculations of the Ps$^{-}$ ion's properties, including energy, annihilation rates, and photodetachment cross-section, advancing understanding of this simple exotic ion.

Findings

Best variational energy: -0.2620050... a.u.

Positronium ion half-life: approximately 4.79 x 10^{-10} seconds.

Photodetachment cross-section estimated with high accuracy.

Abstract

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.