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

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 $\langle r^{k}_{ij} \rangle$ expectation values (where $5 \le k \le 11$), all independent quasi-singular Vinty-type expectation values $\langle \frac{{\bf r}_{ij} {\bf r}_{jk}}{r^{3}_{ij}} \rangle$, the two truly singular $\langle \frac{1}{r^{3}_{ij}} \rangle$ 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.