Calculations on axial dechanneling

Abstract

Abstract An integral equation governing the change with depth of the distribution in transverse energy for an aligned beam is derived. The integral equation is approximated by a diffusion-like equation, in which the diffusion function depends on transverse energy. Thermal vibrations and scattering by electrons contribute to the diffusion. From the transverse energy distribution the yield vs. depth of close encounter processes is evaluated. Our primary aim in obtaining nurnerical solutions to the diffusion equation is to check the validity of simple analytical yield calculations in which diffusion is neglected.