On the stability of the positron's motion near ⟨111⟩ direction of the silicon crystal

The fast charged particle's motion in the crystal under small angle to one of the crystallographic axes densely packed with atoms can be described with high accuracy as the motion in the uniform potentials of the parallel atomic strings that conserves the particle's momentum component parallel to the string axis. The finite motion in the transverse plane in this case is called as the axial channeling. This motion can be both regular (stable) and chaotic (unstable), depending on the presence or absence of the second (in addition to the transverse motion energy) integral of motion. The motion in the axially symmetrical field of the single atomic string conserves the particle's angular momentum projection on the string axis, so the problem has two integrals of motion and hence the particle's motion is regular, periodic or quasiperiodic. The presence or absence of the second integral of motion in the absence of the potential's axial symmetry can be found using the Poincar´e sections method. This paper studies the character of motion of the positron channeling in the [111] direction of the Silicon crystal.