Annihilation of Positrons from Positronium Negative Ione−e+e−

Annihilation of positrons from the positronium negative ion is calculated by a Schroeder six-parameter wave function. The calculation yields a lifetime against two- and three-photon annihilation of 5.02×${10}^{-10\mathrm{}}$ and 5.66×${10}^{-7\mathrm{}}$ sec, respectively. The first value is considerably better than the one given by Ferrell. It is found that the value of the lifetime against two-photon annihilation falls close to the values observed by Bell and Jørgensen in Cs and K, and by Weisberg and Berko in Rb, i.e., in low-density metals. This fact is considered as partial evidence that in such media the positronium ion may be formed. For the two-photon annihilation, a plot of calculated angular correlation of emitted photons and of the momentum distribution function is reported. The angular-correlation function shows the maximum at $\pi -\vartheta$, with $\vartheta =2.0\mathrm{}\times {10}^{-4\mathrm{}}$ rad, the departure from $\pi$ being due to the presence of the spectator electron.