Electron-Positron Pair Production By Photons In Nonuniform Strong Fields

A probability of electron-positron pair production by photons in strong nonuniform fields is derived by applying a model trajectory method in the frame of a semiclassical approach. In addition to the well known invariant field parameter $\chi$, a new invariant parameter $\nu$ is introduced to characterize the nonuniformity of the field. For $\nu \gg 1$, the obtained expression is reduced to the uniform-field approximation while it approaches the Bethe-Heitler formula for $\nu \ll 1$. The pair production is predicted for relatively weak external fields where the uniform-field approximation gives no effect. The theory agrees well with the experimental results of crystal-assisted pair production.