By Valeriy Astapenko

The ebook is dedicated to the trendy conception and experimental manifestation of Polarization Bremsstrahlung (PB) which arises as a result of scattering of charged debris from numerous objectives: atoms, nanostructures (including atomic clusters, nanoparticle in dielectric matrix, fullerens, graphene-like two-dimensional atomic constitution) and in condensed subject (monocrystals, polycrystals, partly ordered crystals and amorphous subject) the current e-book addresses almost always researchers drawn to the radiative techniques throughout the interplay among speedy debris and subject. It will also be helpful for post-graduate scholars focusing on radiation physics and similar fields.

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**Extra resources for Polarization Bremsstrahlung on Atoms, Plasmas, Nanostructures and Solids**

**Sample text**

As seen from Eq. 63, for calculation of the spectral PBs cross-section it is necessary to know the explicit form of the q and q0 functional dependence of Sii . 65) where N is the number of electrons in an atom. The approximate Eq. 65 can be obtained after a number of transformations, taking into account the explicit form of the electron density operator being an operator of shift in the momentum space and corresponding permutation relations. The physical meaning of two summands in Eq. 65 is transparent: the first summand describes processes with ionization of the atomic core, when a transferred momentum is large, in this case the contribution of bound electrons is incoherent and part of energy is carried away by a knocked-on electron.

Analyzing the initial relativistic expression, from which Eq. 31 follows, it can be said that the first summand in the square brackets in Eq. 31 arises from the sum over the positive part of the atomic electron spectrum and describes scattering of an electromagnetic field by the atomic electron current. The second summand in 28 2 Quantum-Electrodynamics Approach to Description of Bremsstrahlung. . Eq. 31 arises after folding of the sum over states of the negative energy spectrum and describes field scattering by the atomic electron charge.

In this range the compensation of a momentum transferred from an IP to an atom due to a photon momentum is possible. As the analysis shows, this is pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ true only for small enough radiation angles: # pa =o % l=Ra ; Ra % pÀ1 a . This inequation follows from the condition of smallness of a momentum transferred to a target during Bs in comparison with an atomic momentum: o ð1 À v0 cosð#ÞÞ pa v0 . Thus in the frequency range of Eq. 57 PBs gains directionality, and in calculation of the process cross-section it is necessary to take into account a photon momentum.