The $(e^{-},e^{+})$-pair annihilation in the bipositronium ${\mathrm{Ps}}_2$ (or $e^{-}{e}^{+}{e}^{-}{e}^{+}$) is considered. In particular, the two-, three-, one-, and zero-photon annihilation rates are determined to high accuracy. The corresponding analytical expressions for these annihilation rates are also presented. By using our most recent and accurate variational wave functions produced for the ground $S(L=0)$ state of the bipositronium ${\mathrm{Ps}}_2$ $(E=-0.5160037754\mathrm{a.u.})$ we have found for the two-photon annihilation rate ${\Gamma }_{2\gamma }\approx 4.66424\times {10}^9{\mathrm{s}}^{-1}$, while ${\Gamma }_{3\gamma }\left({\mathrm{Ps}}_2\right)\approx 1.2022\times {10}^6{\mathrm{s}}^{-1}$, ${\Gamma }_{1\gamma }\approx 1.954\times {10}^{-1}{\mathrm{s}}^{-1}$, and ${\Gamma }_{0\gamma }\approx 2.34\times {10}^{-9}{\mathrm{s}}^{-1}$. Also, a large number of bound state properties have been determined for this system.

• Received 5 January 2005

DOI:https://doi.org/10.1103/PhysRevA.72.014501