Radiationless Annihilation Of Positrons In Lead

A process of positron annihilation without emission of radiation, radiationless or zero-quantum annihilation, has been investigated experimentally. A theory for this phenomenon has also been developed. The 300-keV positrons were focused on a thin lead target by the use of a Siegbahn-Sl\"atis intermediate-image spectrometer mounted with ${\mathrm{Na}}^{22}$ as a positron source. The shell electrons ejected from the lead foil were observed with a lithium-drifted silicon detector mounted immediately behind the foil. We have observed a small peak in the expected energy region of the electron spectrum. This has been attributed to the shell electrons ejected from the lead foil. The effect of target thickness has been examined carefully as an important factor influencing our observations. Using the experimental data obtained, we have attempted to estimate the total cross section of this annihilation process in lead. Our experimental result is ${\ensuremath{\sigma}}_{\mathrm{exptl}}=0.8_{\ensuremath{-}0.3}^{}{}_{}{}^{+0.4}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ ${\mathrm{cm}}^{2}$ as a sum of those for $K\ensuremath{-}K$, $K\ensuremath{-}L$, $K\ensuremath{-}M$, and $L\ensuremath{-}L$ pairs of shell electrons in a lead atom for 300-keV positrons. The calculated cross section we obtained is ${\ensuremath{\sigma}}_{\mathrm{calc}}=0.727\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ ${\mathrm{cm}}^{2}$. Our experimental value is in agreement with the calculated result within the experimental error. The present work has established the experimental evidence for this mode of positron annihilation, and has furthered understanding of the process.