Abstract

The interaction potentials of electrons with the basal and prismatic planes, as well as with the c and \(\left\langle {2\bar {1}\bar {1}0} \right\rangle \) axes in hexagonal close-packed crystals (in particular, in crystals of Be, Sc, Ti, Co, Zn, Y, Zr, Tc, Ru, Cd, and La) at a temperature of 300 K are calculated in the Molière approximation. For comparison, the potentials of electron interaction with the {100} planes and the 〈100〉 axes in cubic crystals of Li, Ca, V, Fe, Cu, Sr, Nb, Mo, Rh, Ag, and Ba with body-centered or face-centered lattices are calculated. The choice of these crystals is due to the fact that the atoms from which they are built are adjacent in the Periodic Table. Calculations show that potential wells, as a rule, are deeper in hexagonal crystals than in cubic ones, both in the planar and axial cases. For relativistic electrons with the Lorentz factor γ = 20, when solving the corresponding Sturm–Liouville problems, the energy levels of transverse motion and the corresponding wave functions are found numerically. The spectra of the spontaneously channeling radiation are also numerically calculated in the dipole approximation for a dispersion-free electron beam moving at zero angle with respect to the corresponding crystallographic plane and axes. It is shown that the frequencies and amplitudes of the spectral peaks, as well as the total intensities of these spectra in crystals with a hexagonal structure, are more efficient for practical use than similar characteristics in cubic crystals.

中文翻译：

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六方结构晶体中相对论电子通道过程中的自发发射

摘要

电子与基面和棱柱面以及c和\(\left\langle {2\bar {1}\bar {1}0} \right\rangle \)的相互作用势在 300 K 的温度下，六方密排晶体（特别是 Be、Sc、Ti、Co、Zn、Y、Zr、Tc、Ru、Cd 和 La 的晶体）中的轴以莫里哀近似计算。为了比较，体心 Li、Ca、V、Fe、Cu、Sr、Nb、Mo、Rh、Ag 和 Ba 立方晶体中电子与 {100} 面和 <100> 轴的相互作用势或面心晶格计算。选择这些晶体是因为构成它们的原子在元素周期表中是相邻的。计算表明，在平面和轴向情况下，六方晶体中的势阱通常比立方晶体中的更深。对于洛伦兹因子 γ = 20 的相对论电子，在求解相应的 Sturm-Liouville 问题时，横向运动的能级和相应的波函数是用数值计算的。自发通道辐射的光谱也在偶极子近似中进行数值计算，用于相对于相应晶面和轴以零角度移动的无色散电子束。结果表明，在具有六方结构的晶体中，光谱峰的频率和幅度以及这些光谱的总强度在实际应用中比立方晶体中的类似特性更有效。