Transmission of 1 - 6-keV positrons through thin metal films

Abstract

We report measurements of the transmission of 1 - 6-keV energy positrons through films of Al, Cu, and Si up to 3000 \AA{} thick. When the thickness is expressed in terms of mass per unit area, the transmission of Cu and Al is found to be the same within \ifmmode\pm\else\textpm\fi{}10%. Within a \ifmmode\pm\else\textpm\fi{}20% precision we observe no effect having to do with the crystallinity of the materials. The median penetration depth of positrons in Al and Cu is found to vary with the energy $E$ as ${E}^{n}$, with $n={1.60}_{\ensuremath{-}0.08}^{+0.15} \mathrm{and} {1.43}_{\ensuremath{-}0.11}^{+0.07}$, respectively. Our measured median penetration depths are significantly less than one would have expected from the calculation of Nieminen and Oliva [R. M. Nieminen and J. Oliva, Phys. Rev. B 22, 2226 (1980)] which seems to indicate the importance of large-angle scattering effects. Our measurements can be combined with independent measurements of the energy dependence of the yield of positronium at a surface [K. G. Lynn, Phys. Rev. Lett. 44, 1330 (1980) and K. G. Lynn and D. O. Welch, Phys. Rev. B 22, 99 (1980)] to obtain values for the positron diffusion constant ${D}_{+}$ in single-crystal metal samples. For example, we find ${D}_{+}(\mathrm{Al})=(0.76\ifmmode\pm\else\textpm\fi{}0.14)$ ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and ${D}_{+}(\mathrm{Cu})=(1.06\ifmmode\pm\else\textpm\fi{}0.20)$ ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The former is in agreement with the deformation-potential calculation of Bergersen et al. B. Bergersen, E. Pajanne, P. Kubica, M. J. Stott, and C. H. Hodges, [Solid State Commun. 15, 1377 (1974)] if the positron effective mass in Al is ${m}_{+}=(1.59\ifmmode\pm\else\textpm\fi{}0.12){m}_{e}$. Finally, we use our measurements to calculate the optimum thickness of transmitting positron moderators for enhancing the brightness of slow positron beams.