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    • br The current of inelastically scattered electrons

    2018-11-05


    The current of inelastically scattered electrons is determined by the density matrix
    The angular brackets in the right-hand side of equality (9) correspond to averaging over the distribution of the scattering centers. If inelasticity is not connected to the excitation of the force centers by which the electrons are scattered elastically, then the T · T* factor can be taken out of the averaging sign. Strictly speaking, the density matrix depends not only on the coordinates r of the scattered particle, but also describes the state of the medium. We shall assume that summation is performed over the final states of the medium; further, this will correspond to cAMPS-Sp, triethylammonium salt with respect to the momentum acquired by the medium in the event of inelastic particle scattering. In turn, the density matrix for the processes in question is determined by the corresponding vertex functions Г:
    Fig. 1 shows diagrams defining the required density matrices. Standard notations are used [3]. Only the crossed diagrams (see Fig. 1) make a contribution to the new type of weak localization. The term in the density matrix ρ(r, r’) corresponding to the crossed diagram has the form
    Main results The results of calculating the orientation dependences for particle motion in an infinite medium were presented and discussed in [3]. In this case, the contribution of the processes described by the crossed diagrams to the total scattering intensity, with respect to the contribution of the processes described by the ladder diagrams, /, can be obtained analytically under fairly general assumptions [3]. If the magnitude of the momentum transferred to the medium during the event of inelastic collision is fixed and not too small compared with the momentum of the particle, the contribution of the crossed diagrams will be written in the following form: where and are the cosines of the angles of particle incidence on the surface and exit from it, with respect to the inner normal, θ is the angle of particle scattering. The dependence of the degree of coherence / on the angle of particle exit from the solid for angles of incidence of about 75° is given for intermediate-energy electrons in Fig. 2 (curve 1). For the dependence presented, we performed summation over all possible momenta transferred during the inelastic collision; the parameter λ/l ≈ 0.1. Curve 2 in Fig. 2 is the result of the computer calculation of the degree of coherence for the same scattering characteristics in the case of quantum transport of electrons emitted by the medium. The energy of these electrons is comparable to that of the inelastically scattered primary electrons. Evidently, the orientation effect for the electrons emitted by the medium (the so-called secondary electrons) is more pronounced. Curve 3 in Fig. 2 shows the results of calculating the degree of coherence for Auger electrons emitted from the solid. For these electrons, this parameter also has a more pronounced orientation dependence.
    Introduction The cerebellum is an important brain region responsible for movement coordination, motor function, muscle tone, balance regulation, and motor learning. The precise coordination of the activity of cerebellar neurons determines the response rate and the integration of movements. Cerebellar conduction pathways play a major role in controlling motor function, since they transfer information to other regions of the nervous system [1]. The only efferent pathway connecting the cerebellar cortex to its deep nuclei is via the axonal projections of Purkinje cells (PCs), which are large GABAergic neurons, i.e., cells of the central nervous system whose major inhibitory neurotransmitter is the γ-aminobutyric acid (GABA). Thus, PCs are the key elements of the cerebellar cortex, with the correct functioning of these neurons responsible for motor speed and coordination [2]. Indeed, PC damage leads to disrupted coordination of the movements of different muscles, which is a clinical symptom of neurodegenerative diseases such as autosomal dominant cerebellar ataxia (ADCA) [3]. Almost complete PC degeneration is found in the majority of ataxia patients in the last stages of the disease [4]. However, experimental studies have shown that ADCA symptoms in the early stages are possibly caused not by cell degeneration but by the disruption of the biophysical and physiological properties of PCs. The evidence supporting this hypothesis is the decrease in regular pacemaking of PCs detected in ADCA mouse models in cases of episodic ataxia type 2 (EA2) [5], as well as in some types of spinocerebellar ataxia (SCA) [6,7]. Based on these findings, it was suggested that medications capable of restoring regular PC activity may have a positive therapeutic effect on patients.