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

Abstract

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.