The Photoelectric Effect for High Energy Quanta

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 hν greater than the proper energy mc² of the electron is considered. The total photo-absorption from the K-shell is found in this way to be approximately ${{τ}}K=1.16×{}{{10}^{{-}23}{Z}⁵{λ}·{}R}{{{α}}^{2{{α}}²}{e}^{{α}({π}{-}2{α})}},$ where $R{~}1+{7m{c}²}{3h{ν}}{→}1$, as ${ν}{→}{∞}$, and ${α}={2{π}{e}²Z}{hc}$. The factor depending on ${α}$ is seen to modify the result appreciably for heavy elements, so that for lead, and the gamma-rays from Th C", ($Z=82$, ${λ}=4.7$ X.U.), ${{τ}}K=1.1×{}{10}^{{-}24}$ ${cm}²$. The agreement with experiment is satisfactory.