Polarization bremsstrahlung of a fast charged particle on a Thomas-Fermi atom

An universal description of the polarization bremsstrahlung of a fast charged particle on a multi-electron atom (Z ≫ 1, Z is the nuclear charge) is obtained using the local electron density method and the Thomas-Fermi statistical model. It is shown that the cross section of the process can be represented in the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$d\sigma ^{PB} (\omega ) = Z^2 d\tilde \sigma ^{PB} (\nu )$$ \end{document}, where the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$d\tilde \sigma ^{PB} (\nu )$$ \end{document} exhibits approximate scaling with respect to the parameter ω/Z = v, and the corresponding R factor (ratio of the cross sections in the polarization and ordinary channels) is greater than 1 in a wide range of frequencies and reaches its maximum value at frequencies ω ≈ ZRy. It is demonstrated that in the frequency range pac < ħω < γ2pac (γ is the relativistic factor, pa is the characteristic momentum of the atomic electrons, and c is the speed of light) the angular distribution of the polarization bremsstrahlung of a relativistic charged particle undergoes narrowing due to the compensation, by the momentum of the emitted photon, of the momentum transfer from the incident particle to the atomic core.