Bound state properties and positron annihilation in the negatively charged Ps${}^{-}$ ion. On thermal sources of fast positrons and annihilation $\gamma$-quanta in our Galaxy

Abstract

The total energy and other bound state properties of the ground (bound) $1^{1}S$-state in the Ps${}^{-}$ (or $e^{-}{e}^{+}{e}^{-}$) ion are determined to very high accuracy. Our best variational energy for the ground state in this ion equals $E$ = -0.26200507023298010777040211998 $a.u.$, which is the lowest variational energy ever obtained for this ion. By using our highly wave functions we evaluated (to very high accuracy) a number of different expectation values (or properties) of the Ps${}^{-}$ ion which have never been determined in earlier studies. This includes a number of $⟨r_{ij}^k⟩$ expectation values (where $5\le k\le 11$), all independent quasi-singular Vinty-type expectation values $⟨\frac{{\mathbf{r}}_{ij}{\mathbf{r}}_{jk}}{r_{ij}^3}⟩$, the two truly singular $⟨\frac{1}{r_{ij}^3}⟩$ expectation values, etc. Our highly accurate expectation values of the electron-positron delta-function of the Ps${}^{-}$ ion we have evaluated (to very high accuracy) the rates of two-, three-, four- and five-photon annihilation. We also discuss thermal sources of the fast positrons and annihilation $\gamma$-quanta located in our Galaxy.

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