Volume Reflection and Refraction of Relativistic Particles in Bent Crystals

The quasi-channeling of positive and negative relativistic particles in a bent crystal is studied using the classical deflection function. It was shown that the potential scattering in a central field of bounded ring-like potentials may produce the ``reflected'' and ``refracted'' fractions of scattered particles. For particles with positive charge the ``reflected'' fraction is mainly presented; at the same time we predict that for particles with negative charge the ``refracted'' fraction should dominate. The effect of ``empty core'' for central scattering is also discussed. The average deflection angles for volume ``reflection'' and ``refraction'' are derived for accepted potential model of the crystal. The calculated average ``reflection'' angle is in satisfactory agreement with recent experimental data \cite{ivanov_2006}