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>>1, the obtained expression is reduced to the uniform-field approximation while it approaches the Bethe-Heitler formula for nu<<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.