Multi-photon annihilation in the negatively charged positronium ion

Abstract

Abstract The total energy and other bound state properties of the ground (bound) 11 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 〈 r ij k 〉 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.