Relativistic Calculation of Polarizational Bremsstrahlung Spectra

Abstract

A formalism for the full relativistic treatment of the polarizational bremsstrahlung formed in collision of a charged particle with a many-electron target is developed. The multipole series for amplitude and cross section are evaluated. The presented results of numerical computation of polarizational bremsstrahlung cross sections and angular distributions show the importance of the relativistic and higher-multipole effects in the case of relativistic collision with a high-Z target. The logarithmic growth of relativistic cross section with increasing incident energy is demonstrated. The calculations are performed on the basis of the nonrelativistic and relativistic algorithms and compared with each other and with available experimental data.

Polarizational bremsstrahlung in non-relativistic collisions

“…Even within this framework the accurate calculation of the generalized polarizability α(ω, q) is not a simple task. Apart from the case of a hydrogen atom (or hydrogenlike ion) where the analytical evaluation is possible [11,40,77] one has to use more sophisticated approaches to calculate this quantity. The methods known to us include the the Hartree-Fock based calculations with [22, 24, 25, 60-63, 66, 72] and without [26] the inclusion of many-body corrections, the approach based on the local-density approximation (see [100] and references therein).…”

“…Various methods of calculation of the generalized polarizability α(ω, q) in the ωregions in vicinities of the ionization potentials of the atomic subshells as well as in the limit ω ≫ I 1s have been already discussed above in the paper. Here we want to mention the approach, developed recently [69,77], which is very effective for the description of the dynamic response in the photon energy range corresponding to the ionization potentials of the the K-and L-atomic shells. In this case the electrons of these shells provide the main contribution to the polarizational BrS cross section.…”

“…A general approach to consider the BrS process (both the ordinary and the polarizational) in collisions with many-electron targets is based on a consistent application of quantum mechanics and quantum many-body theory. The main results obtained by using this approach include: (a) application of the many-body theory for accurate calculations of the dynamic generalized polarizability of the target [60][61][62][63][64] (b) development of the methods for approximate treatment of of the dynamic response of the target [65][66][67][68][69][70], (c) calculation of the total BrS spectra of in collisions of nonrelativistic electrons on many-electron atoms over wide range of emitted photon energies including the regions of giant resonances [71][72][73][74], (d) theoretical description of the PBrS in collisions of slow atomic particles and in collisions involving atoms in the excited states [75][76][77], (e) numerical calculations of inelastic BrS [78,79], (f) theoretical and numerical description of the BrS process in electron-cluster collisions [80][81][82][83][84], (g) the full relativistic description of the BrS in a charged particle-atom collision [85][86][87].…”

Relativistic effects in polarizational bremsstrahlung

“…The role of the relativistic effects mentioned above was studied in [4][5][6][7][8][9][10][11][12][13][14] in various collisions of isolated atomic particles. In this paper we review the results obtained in the cited papers.…”

“…The theory of PBrS formed in a collision of a charged particle with a manyelectron atom/ion was developed further in the papers [11][12][13][14] where the fully relativistic formalism and the results of numerical calculations were presented. The formalism developed in these papers accounts for the relativistic effects of all types mentioned above (with the exception for the Doppler shift and abberation which are irrelevant in the case of a structureless projectile).…”