Determination and applications of enhancement factors for positron and ortho-positronium annihilations

Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the 1s electron in H, He⁺, He, Li²⁺, and Li⁺. The enhancement factor for a free positron annihilating with He⁺ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of 1.47a₀ for Ps-He scattering. Further, enhancement factors for e⁺-Ne and e⁺-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of 1.46a₀ for Ps-Ne scattering and 1.75a₀ for Ps-Ar scattering.