Multi-photon annihilation in the negatively charged positronium ion

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=-0.26200507023298010777040225 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 large number of different expectation values (or properties) of the Ps(-) ion which have never been considered in earlier studies. This includes a number of arij nk expectation values (where 5 <= k <= 11), all independent quasi-singular < r(ij)r(jk) / r(ij)(3) > and singular < 1/ r(ij)(3)> expectation values, etc. Our highly accurate expectation values of the electron-positron delta-function of the Ps(-) ion are used to evaluate (to very high accuracy) the rates of two-, three-, four- and five-photon annihilation. The numerical values of these rates provide the highly accurate and complete solution of the multi-photon annihilation in the negatively charged positronium ion.