Momentum-density calculations for axial channeling in thin crystals

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Abstract
The elements of continuum-model axial channeling are discussed with an emphasis on the depth-dependent phase-space density. This density, which is the joint spatial-momentum density, does not contain effects of thermal vibration or electron multiple scattering, but does contain the ordered nature of the continuum strings. Representations for the depth-dependent momentum density are derived, and two approximations for its determination are developed. The angular dependence of the momentum density is studied using these approximations, and the results are compared with recent data from axial-channeling transmission experiments in thin crystals. The agreement between theory and experiment is quite good.