Quantum theory of channeling. Contribution of multiple scattering of channeled particles by electrons to the dechanneling rate

The principles of nonequilibrium statistical thermodynamics are used to derive some relations of the kinetic theory of dechanneling. The rate of dechanneling, regarded as a process of transition of a particle into an above-barrier state, is determined by Kubo's relation. The Green's function method is used to obtain the corresponding transport equation (of Kolmogorov type), which takes into account simultaneously the coherent nature of the beam diffraction in the regular single crystal and the inelastic scattering of channeled particles on electrons. An analytic solution to this equation is found on the class of confluent hypergeometric functions, and this solution is used to calculate $R_e$, the rate of dechanneling due to multiple scattering of the particles. It is shown that up to terms of second order in the interaction potential the constant $R_e$ is inversely proportional to the relaxation time $\tau_e$ of the system. The calculation of $\tau_e$ takes into account collisions of the channeled particles with electrons (the model of a free electron gas is used) and transitions accompanying these collisions between the levels of the transverse motion of the particles.