The Photoelectric Effect for High Energy Quanta

Abstract

The relativistic quantum electrodynamics is rigorously applied to calculate the cross section for photoelectric absorption of a Dirac electron in the field of a nucleus (of charge Ze). The case of quantum energies $h\ensuremath{\nu}$ greater than the proper energy $m{c}^{2}$ of the electron is considered. The total photo-absorption from the $K$-shell is found in this way to be approximately ${\ensuremath{\tau}}_{K}=1.16\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}23}{Z}^{5}\ensuremath{\lambda}\ifmmode\cdot\else\textperiodcentered\fi{}R}{{\ensuremath{\alpha}}^{2{\ensuremath{\alpha}}^{2}}{e}^{\ensuremath{\alpha}(\ensuremath{\pi}\ensuremath{-}2\ensuremath{\alpha})}},$ where $R\ensuremath{\sim}1+\frac{7m{c}^{2}}{3h\ensuremath{\nu}}\ensuremath{\rightarrow}1$, as $\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\infty}$, and $\ensuremath{\alpha}=\frac{2\ensuremath{\pi}{e}^{2}Z}{\mathrm{hc}}$. The factor depending on $\ensuremath{\alpha}$ is seen to modify the result appreciably for heavy elements, so that for lead, and the gamma-rays from Th C", ($Z=82$, $\ensuremath{\lambda}=4.7$ X.U.), ${\ensuremath{\tau}}_{K}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$. The agreement with experiment is satisfactory.