Elementary Process Of Bremsstrahlung Research Articles

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

BREMS: A program for calculating spectra and angular distributions of bremsstrahlung at electron energies less than 3 MeV

This work describes a program that implements the method developed by Tseng and Pratt in the 1970s for exact screened calculations of atomic-field bremsstrahlung. The calculation method is based on the relativistic partial-wave formulation describing interaction of the incident electron with an arbitrary central potential of the neutral target atom. The set of Fortran-90 codes BREMS has been written with the aim of creating a comprehensive library of spectra and shape functions of unpolarized atomic-field bremsstrahlung for all chemical elements and for the approximate range of the incident electron energy from 10 eV to 3 MeV on a dense energy grid, using the best theory available. Several examples of using this software and its verification against the published data calculated using the same theory are provided. BREMS can be run on modern personal computers, with processing times from several minutes to several hours, depending on the user-specified values of the atomic number, incident electron energy, and photon energy, as well as on the accuracy requested. Program summaryProgram title: BREMSProgram Files doi: http://dx.doi.org/10.17632/mvd57skzd9.1Licensing provisions: GNU General Public License v3Programming language: Fortran 90Nature of problem: The atom is described as a static spherically symmetrical charge distribution of infinite mass. The elementary process of bremsstrahlung is described as a one-electron transition in the field of the neutral atom with a point-like nucleus. The atom is described by a central potential. The singly and doubly differential cross sections of bremsstrahlung are calculated using the relativistic partial wave formulation, which is currently the best theory for calculating the cross sections of unpolarized atomic-field bremsstrahlung.Solution method: The set of codes BREMS solves the Dirac equation with one of three possible types of the interaction potential: 1) the point-Coulomb potential (unscreened nucleus), 2) the Thomas–Fermi–Czavinsky potential, 3) the Kohn–Sham potential. It is also possible to use an arbitrary interaction potential specified by the user in tabular format. The wave functions are expanded in partial wave series and the radial integrals are calculated numerically. The photon energy spectrum and the angular distribution of bremsstrahlung photons are expressed in terms of the mentioned radial matrix elements, resulting in an infinite series, which must be truncated at a predefined value of the absolute value of the quantum number κ. A partial-wave interpolation method is applied in order to reduce the number of radial integrals that have to be calculated. The truncation error is decreased by extrapolation of the differential cross sections as functions of the number of terms retained in the truncated series.Additional comments: (i) Restrictions: Although there is no explicit limitation on the incident electron energy in the code of BREMS, it is currently applicable only at electron energies that are not greater than approximately 3 MeV. At the low-energy end of the spectrum, the single-electron approximation may not be sufficiently accurate due to an increased importance of the many-electron effects at electron energies of the order of 100 eV or lower.(ii) Unusual features: Multiple precision (MP) and quadruple precision (QP) arithmetic are used in several stages of the calculation in order to eliminate the rounding errors due to strong cancellation of terms in the alternating series. The capability of the MP system to change the precision level at runtime is used to optimize the precision level automatically and thus to decrease the computation time.

Validity of sum rules for the polarization transfer in electron bremsstrahlung

The polarization correlations, which describe the spin transfer from a high-energy spin-polarized electron to the photon in the elementary process of bremsstrahlung induced by strong potentials, obey a strict sum rule in the case of coplanar emission. The proof is carried out within the relativistic partial-wave approach. Further sum estimates are obtained by means of a variational principle under the sole condition that the transition amplitude is linear in the electron wavefunctions and in the photon field. Numerical sum rule results are given for light and heavy bare target atoms in the energy range 1–10 MeV.

The polarization of bremsstrahlung from radiative ionization induced by relativistic highly charged projectiles

Based on inverse kinematics the close relation between radiative electron capture to the projectile continuum, calculated within the impulse approximation, and electron–nucleus bremsstrahlung is shown. Particular emphasis is laid on the short-wavelength limit corresponding to cusp-electron emission in the target frame of reference. Differential cross sections and the degree of photon polarization are calculated for the coincident emission of electron and photon. Coplanar and non-coplanar geometries are considered, and the polarization is compared with that obtained from experiments on the elementary bremsstrahlung process and on radiative electron capture to bound states.

Photon polarization and spin asymmetry in the elementary process of bremsstrahlung

Experimental and theoretical results are reviewed concerning the photon polarization and spin asymmetry in the elementary process of bremsstrahlung. In electron–photon coincidence experiments using an unpolarized primary beam (300 keV) the electron–nucleus bremsstrahlung was found to be almost completely linearly polarized. The same behavior was found in electron–electron bremsstrahlung. By using a transversely polarized electron beam the photon emission asymmetry was measured for fixed direction of the outgoing electrons.

Asymmetry of bremsstrahlung from transversely polarized electrons

By using an electron-photon coincidence method the photon emission asymmetry in the elementary process of bremsstrahlung from transversely polarized electrons was measured. For an electron beam of 300 keV incident on a gold target the asymmetry for spin up and down of the primary beam was measured for fixed direc-tions of the outgoing electrons and photons as a function of the energy split. Asymmetries up to 30% were found. The measurements are a proper test for theories going beyond the first Born approximation.

Photon emission asymmetry in the elementary process of bremsstrahlung from transversely polarized electrons.

By using an electron-phonon coincidence method the photon emission asymmetry in the elementary process of bremsstrahlung from transversely polarized electrons was measured for fixed directions of the outgoing electrons and coplanar geometry. For an electron beam of 300 keV incident on a gold target, emission asymmetries up to 35% were found. Even in the case of no deflection of the decelerated outgoing electrons a nonzero photon emission asymmetry was observed. The measurements are a proper test for theories going beyond the first Born approximation.

Measurement of the photon linear polarization in the elementary bremsstrahlung process

In an electron-photon coincidence experiment the linear polarization of atomic-field bremsstrahlung was measured for a fixed direction of outgoing electrons. A polarization of P = -0.96 ± 0.32 was found which is in agreement with theoretical calculation. Electrons of 300 keV are used, incident on a carbon target.

Calculation of Bremsstrahlung Cross Sections with Sommerfeld-Maue Eigenfunctions

A formula for the differential cross section of bremsstrahlung is calculated with the aid of Sommerfeld-Maue eigenfunctions, i.e., under the assumption of a pure Coulomb field and low atomic numbers ($\ensuremath{\alpha}Z\ensuremath{\ll}1$). This expression is valid for all energies of both electrons and photons, and it is shown that the previously well-known formulas of Sommerfeld, Sauter, Bethe, Heitler, Scherzer, and Bethe and Maximon are contained as special cases. Hence this cross section is correct for high electron energies and, apart from a small spin correction, for nonrelativistic energies even if $\ensuremath{\alpha}Z\ensuremath{\ll}1$ is not satisfied. The formula has been programmed, and in addition total cross sections have been obtained by numerical integration over the angles of the emitted electrons and photons. Comparison with the Born approximation allows derivation of the Coulomb correction. Several cases of interest are compared with experiment, in particular the elementary bremsstrahlung process itself, for which experimental results are now available.