Model solution for volume reflection of relativistic particles in a bent crystal

TL;DR

This paper presents an analytical model for volume reflection of relativistic particles in bent crystals, deriving explicit formulas for particle trajectories and deflection angles, and compares these with experimental and simulation data.

Contribution

The paper introduces exact analytic expressions for particle trajectories in a parabolic potential model, including asymptotic formulas for deflection angles and beam profiles, considering both charge types.

Findings

Analytic expressions match experimental data for positive charges.

Negative charges exhibit rainbow scattering and orbiting effects.

Model predictions are robust against multiple scattering effects.

Abstract

For volume reflection process in a bent crystal, exact analytic expressions for positively- and negatively-charged particle trajectories are obtained within a model of parabolic continuous potential in each interplanar interval, with the neglect of incoherent multiple scattering. In the limit of the crystal bending radius greatly exceeding the critical value, asymptotic formulas are obtained for the particle mean deflection angle in units of Lindhard's critical angle, and for the final beam profile. Volume reflection of negatively charged particles is shown to contain effects of rainbow scattering and orbiting, whereas with positively charged particles none of these effects arise within the given model. The model predictions are compared with experimental results and numerical simulations. Estimates of the volume reflection mean angle and the final beam profile robustness under multiple scattering are performed.