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

Abstract

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, ${\mathrm{He}}^{+}$, He, ${\mathrm{Li}}^{2+}$, and ${\mathrm{Li}}^{+}$. The enhancement factor for a free positron annihilating with ${\mathrm{He}}^{+}$ 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 $1.47{a}_{0}$ 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 $1.46{a}_{0}$ for Ps-Ne scattering and $1.75{a}_{0}$ for Ps-Ar scattering.