The Production of a Positron-Electron Pair in the Electrostatic Field of an Electron

The production of positron-electron pairs in the electrostatic field of an electron is considered. In spite of the light mass of the recoil electron and the exchange effect between the two electrons, the process is quite similar to ordinary pair production. For the limiting case of high energy $\gamma$-rays, the ratio of triplet production to pair production should vary as $\frac{1}{Z}$. For $\frac{h\nu }{m{c}^2}<30\mathrm{}$, pair production will have a relatively greater cross section for all values of $Z$, the nuclear charge.