One-photon annihilation in the ${\mathrm{Ps}}^{\mathrm{-}}$ ion and the angular (${\mathit{e}}^{\mathrm{-}}$,${\mathit{e}}^{\mathrm{-}}$) correlation in two-electron ions

Various properties of the ${\mathrm{Ps}}^{\mathrm{-}}$ ion in its bound ground ${(}^1$S) state are calculated from a very accurate explicitly correlated wave function. From the expectation value for the triple delta function 〈${\mathrm{\delta }}_{321}$〉=‖ψ(0,0,0)${\mathrm{\Vert }}^2$ we estimate the one-photon annihilation rate ${\mathrm{\Gamma }}_{\gamma }$ in the ${\mathrm{Ps}}^{\mathrm{-}}$ ion and show that ${\mathrm{\Gamma }}_{\gamma }$≪${\mathrm{\Gamma }}_{3\gamma }$≪${\mathrm{\Gamma }}_{2\gamma }$. The statistical angular correlation coefficients are analyzed for the series of two-electron ions (${\mathit{e}}^{\mathrm{-}}$ ${\mathit{e}}^{\mathrm{-}}$ ${\mathit{Z}}^{+}$) which includes ${\mathrm{T}}^{\mathrm{-}}$, ${\mathrm{D}}^{\mathrm{-}}$, ${\mathrm{H}}^{\mathrm{-}}$, ${\mathrm{Mu}}^{\mathrm{-}}$, and ${\mathrm{Ps}}^{\mathrm{-}}$.