Quasicharacteristic radiation of relativistic electrons at orientation motion in lithium halides crystals along charged planes and axes

Calculation of spontaneous radiation during channeling of relativistic positrons in non-chiral nanotubes using a quadratic approximation

“…where 𝑑 = 3𝑑 0 for CNTs of type (𝑛, 0) and 𝑑 = 𝑑 0 √ 3 for CNTs of type (𝑛, 𝑛), 𝑑 0 ≈ 1.44 𝐴 (see, for example, [6]); 𝐾 0,1 (𝑥) -MacDonald functions of zero and first order. Using equation (2.1), we calculate in relative coordinates ζ = ρ/𝑅 (the radii for CNTs of type (𝑛, 0) are equal to 𝑅 = 𝑑 0 √ 3𝑛/2π, and for CNTs of type (𝑛, 𝑛) respectively 𝑅 = 3𝑑 0 𝑛/2π [6]) the interaction potentials of channeled positrons with the inner walls of CNTs of types (8, 0), (10, 0), (12, 0) and (8,8), (10,10), (12,12). Figures 1a, b illustrates the interaction potentials for CNTs of types (10, 0) and (10, 10), respectively.…”

Peculiarities of Channeling and Generated Radiation of Relativistic Electrons in the Main Charged Axes of Lithium Hydride Crystal

“…This formula was obtained in the dipole approximation on the basis of [10] by analogy with the corresponding expressions in [8,12]. Here…”

“…To get more short-wave and more intensive short wave radiation (e.g. see spectral short wave dependencies for lithium halides crystals in [8]) in the given paper the analogous consideration for relativistic electrons with Lorentzfactors γ  50, 75, 100 (   25.6, 38.3, 51.1 MeV) is carried out in the main charged [110] axes in LiH crystal at T  300, 600, 900 K. It is necessary to note that channeling along the direction [110] is interesting because of the fact that in the charged Li + -[110] -axes, potential wells depths almost in 50% are formed by a long range Coulomb interaction with crystal ions and in the charged H --[110] -axes the inversion of potential wells into potential barriers occurs with temperature changing.…”

Investigation of channeling and radiation of relativistic electrons in charged planes of the crystals with zinc blende structure

“…At the calculation of planar interaction potentials in the crystals with a zinc blende structure, oneparticle potentials for positively and negatively charged ions can be written using the following Moliere approximation: φ ± (r) = {[Z ± − (±α)] e/r } 3 j=1 α j exp −β j r/b ± ± αe/r, where α j and β j we get, for example, from [4], b ± = 0, 8853Z −1/3 ± a 0 -Tomas-Fermi radii, correspondingly, for positively and negatively charged ions, a 0 -Bohr radius, Z ± -atomic numbers of their nuclei, αthe crystal ionicity degree [5]. Further we execute standard procedures of averaging by planes and by thermal oscillations [4] (here the contribution from long-range Coulomb potentials is taken into account on the basis of the technique described in [3,6]). As a result, we find electrons interaction potentials with main charged (100) and (111) planes presented in figure 1a in a conditional cubic cell (see, for example, [7]) by blue and green colors, correspondingly.…”

“…In [1,2] it is shown that the channeling of relativistic electrons in charged planes of crystals with a zinc blende structure has a number of interesting peculiarities. In particular, at the channeling in main charged (100) and (111) planes, as in the case of the channeling in the charged (111) planes in NaCl-type crystals (see, for example, [3]) due to the Coulomb terms in one-particle interaction potentials, there is a transformation of potential wells (there is a deepening of them in positively charged planes and accordingly decrease of the depths in negatively ones). At the change of the type of used crystal plane from the main low-index to the high-index charged planes, the potential wells transform from non-unimodal to unimodal ones (similar changes are also observed at increase of crystal temperature).…”