Diffusion length of positrons and positronium investigated using a positron beam with longitudinal geometry

Abstract

Positronium emission from single crystalline ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, $\mathrm{MgO}$ and vitreous $a{\text{\ensuremath{-}}\mathrm{SiO}}_{2}$ surfaces was studied as a function of the positron implantation energy $E$ by means of Doppler broadening spectroscopy and Compton-to-peak ratio analysis. When the Ge-detector is in-line with the positron beam, the emission of para-positronium yields a red-shifted fly-away peak with intensity ${I}_{\mathrm{pPs}}^{\mathrm{e}}$. An analysis of ${I}_{\mathrm{p}\mathrm{P}\mathrm{s}}^{\mathrm{e}}$ versus $E$ for ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and $\mathrm{MgO}$ where no $\mathrm{Ps}$ is formed in the bulk $({f}_{\mathrm{Ps}}=0)$ results in positron diffusion lengths ${L}_{+}({\mathrm{Al}}_{2}{\mathrm{O}}_{3})=(18\ifmmode\pm\else\textpm\fi{}1)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and ${L}_{+}(\mathrm{MgO})=(14\ifmmode\pm\else\textpm\fi{}1)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and efficiencies for the emission of $\mathrm{Ps}$ by picking up of a surface electron of ${f}_{pu}({\mathrm{Al}}_{2}{\mathrm{O}}_{3})=(0.28\ifmmode\pm\else\textpm\fi{}0.2)$ and ${f}_{pu}(\mathrm{MgO})=(0.24\ifmmode\pm\else\textpm\fi{}0.2)$. For $a{\text{\ensuremath{-}}\mathrm{SiO}}_{2}$ the bulk $\mathrm{Ps}$ fraction is ${f}_{\mathrm{Ps}}(a{\text{\ensuremath{-}}\mathrm{SiO}}_{2})=(0.72\ifmmode\pm\else\textpm\fi{}0.01)$, ${f}_{pu}(a{\text{\ensuremath{-}}\mathrm{SiO}}_{2})=(0.12\ifmmode\pm\else\textpm\fi{}0.01)$ and the diffusion lengths of positrons, para-positronium and ortho-positronium are ${L}_{+}({\mathrm{SiO}}_{2})=(8\ifmmode\pm\else\textpm\fi{}2)\mathrm{nm}$, ${L}_{\mathrm{pPs}}({\mathrm{SiO}}_{2})=(14.5\ifmmode\pm\else\textpm\fi{}2)\phantom{\rule{0.2em}{0ex}}\mathrm{nm}$ and ${L}_{\mathrm{oPs}}({\mathrm{SiO}}_{2})=(11\ifmmode\pm\else\textpm\fi{}2)=\mathrm{nm}$. Depending on the specimen-detector geometry the emission of $\mathrm{Ps}$ at low implantation energy may cause either an increase or a decrease of the width of the annihilation line shape at low implantation energies.