Scattering of high-energy positively charged particles in ultrashort oriented silicon crystal

In this work, the process of scattering of high-energy positively charged particles in the field of atomic planes of an ultrashort silicon crystal was studied. In the parabolic potential approximation of atomic planes, analytical expressions are found for the dependence of the coordinates and velocities of particles in a crystal on time and initial conditions. The relationship between the particle incidence angle on the crystal and its deflection angle has also been determined. It is shown that, under certain conditions, a beam can be split by an ultrashort crystal into two beams diverging at an angle equal to twice the angle of planar channeling.