Measurements of the critical angle for channeling of heavy ions in copper using characteristic X-ray generation

Measurements are presented of ψ1/2, the width of the dip in the yield of CuL X-rays when Ne+, Ar+, Kr+ and Xe+ of 150–350 keV are channeled in the <110> axis of copper. Absorption of the X-rays and the slowing down of the beam are shown to limit the depth from which the detected X-rays can come. The magnitude of the effect of multiple scattering on the measured values of ψ1/2 is shown to be small for all the projectiles except nech. The data has a dependence on (Z 1/E) which is intermediate between that of the critical angles ψ1 and ψ2. A numerical calculation of critical angle gives good agreement with the data. At low energy the calculation uses a potential which is a sum of screened Coulomb and Born-Mayer terms; at higher energy screened Coulomb alone is adequate. A simple analytical expression for the critical angle, based on a 1/r2 atomic potential, may be used as an approximation to the results.