Mean volume reflection angle

Abstract

The mean volume reflection angle of a high-energy charged particle passing through a bent crystal is expressed as an integral involving the effective interplanar potential over a single crystal period. Implications for positively and negatively charged particles, and silicon crystal orientations (110) and (111) are discussed. A generic next-to-leading-order expansion in the ratio E/R of the particle energy E to the crystal bending radius R is given. For positively charged particles, the dependence of the mean volume reflection angle on E/R proves to be approximately linear, whereas for negatively charged particles the linear behaviour is modified by an E/R-dependent logarithmic factor. Up-todate experimental data are confronted with predictions based on commonly used atomic potentials.