Constant field approximation for the crystal-assisted pair-creation process

Abstract

The electron-positron production rate for the newly predicted crystal-assisted pair creation process is proportinal to squared matrix elements. Each matrix element is governed by the overlap of a channeled electron wavefunction and the wavefunction of a positron which is repelled by the same channeling potential. Closed form expressions for these matrix elements can be obtained by linearizing the channeling potential in the neighborhood of the classical turning points. Results obtained from the linear potential approximation were compared with more accurate numerical results for photons directed along the 〈110〉 axis of diamond. Agreement to within a factor of two was obtained over a wide range of incident energies. These approximate calculations have been extended to yield predictions for the crystal-assisted pair production rate for a number of different crystals, different axis orientations, and a variety of temperatures.