Martin J. Berger

ITS: the integrated TIGER series of electron/photon transport codes-Version 3.0

The ITS system is a powerful and user-friendly software package permitting state-of-the-art Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. Version 3.0 is a major upgrade of the system with important improvements in the physical model, variance reduction, I/O, and user friendliness. Improvements to the cross-section generator include the replacement of Born-approximation bremsstrahlung cross section with the results of numerical phase-shift calculations, the addition of coherent scattering and binding effects in incoherent scattering, an upgrade of collisional and radiative stopping powers, and a complete rewrite to Fortran 77 standards emphasizing Block-IF structure. Improvements in the Monte Carlo codes are also described.<<ETX>>

Bremsstrahlung spectra from electron interactions with screened atomic nuclei and orbital electrons

Abstract Through the synthesis of various theoretical results, a comprehensive set of bremsstrahlung cross sections (differential in the energy of the emitted photons) has been prepared. The set includes results for electrons with energies from 1 keV to 10 GeV incident on neutral atoms with atomic numbers Z = 1 to 100. For bremsstrahlung in the Coulomb field of the atomic nucleus, use was made of (a) results of Pratt, Tseng, and collaborators based on numerical phase-shift calculations for the screened Coulomb potential at energies below 2 MeV, and (b) the analytical high-energy theory (with Coulomb corrections) of Davies, Bethe, Maximon and Olsen at energies above 50 MeV, supplemented by the Elwert Coulomb correction factor and the theory of the high-frequency limit given by Jabbur and Pratt. In the high-energy region, the effect of screening was included with use of Hartree-Fock atomic form factors. A numerical interpolation scheme, applied to suitably scaled cross sections, was used to bridge the gap between the low-energy and high-energy theoretical results, and thus to obtain improved cross sections in the intermediate-energy region 2 to 50 MeV. Bremsstrahlung in the field of the atomic electrons was calculated according to the theory of Haug, combined with screening corrections derived from Hartree-Fock incoherent scattering factors. The paper also contains numerous comparisons between calculated and measured bremsstrahlung spectra, which indicate generally good agreement.

Bremsstrahlung energy spectra from electrons with kinetic energy 1 keV–10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z = 1–100☆

A comprehensive set of bremsstrahlung cross sections (differential in the energy of the emitted photons) is tabulated. The set includes results for electrons with energies from 1 keV to 10 GeV incident on neutral atoms with atomic numbers Z = 1 to 100. For bremsstrahlung in the Coulomb field of the atomic nucleus, use was made of (a) results of Pratt, Tseng, and collaborators based on numerical phase-shift calculations for the screened Coulomb potential at energies below 2 MeV; and (b) the analytical high-energy theory (with Coulomb corrections) of Davies, Bethe, Maximon, and Olsen at energies above 50 MeV, supplemented by the Elwert Coulomb correction factor and the theory of the high-frequency limit given by Jabbur and Pratt. In the high-energy region, the effect of screening was included by the use of Hartree-Fock atomic form factors. A numerical interpolation scheme, applied to suitably scaled cross sections, was used to bridge the gap between the low-energy and high-energy theoretical results, and thus to obtain improved cross sections in the intermediate-energy region 2 to 50 MeV. Bremsstrahlung in the field of the atomic electrons was calculated according to the theory of Haug, combined with screening corrections derived from Hartree-Fock incoherent scattering factors.

Density effect for the ionization loss of charged particles in various substances

The density-effect correction δ(β) for the ionization energy loss of charged particles has been evaluated as a function of the particle velocity for a total of 278 substances, including 98 cases of elements of the periodic table (12 gases and 86 condensed materials, including liquid hydrogen and graphite of three different densities) and 180 chemical compounds and substances of biological interest (13 gases and 167 liquid or solid substances). In the calculations, up-to-date values of the mean excitation potential I and of the atomic absorption edges hvi were employed as input data for the general equations for δ(β) previously derived by Sternheimer.

Energy deposition by auroral electrons in the atmosphere

Abstract The spatial distribution of the energy deposited by electrons in the atmosphere has been calculated by the Monte Carlo method. The distribution has been obtained as a function of the altitude and of the radial distance from the axis of the incident electron beam. The calculations take into account the deflection of the electrons by the geomagnetic field, and the scattering and slowing down due to multiple Coulomb interactions with atomic nuclei and orbital electrons. The assumed conditions were: 1. (1) a semi-infinite air medium, extending downwards from a height of 300 km, with a composition and density corresponding to that of the CIRA (1965) Mean Atmosphere 2. (2) a vertical magnetic field with a strength of 0.6 G 3. (3) monoenergetic incident electron beams that are symmetric about a chosen field line 4. (4) incident electron energies between 20 keV and 2 keV 5. (5) various incident pitch-angles between 0° and 90°, or a pitch-angle distribution corresponding to an incident flux isotropic over the downward hemisphere. Calculations made with the same program, for a constant-density medium and no magnetic field, give good agreement with the results of laboratory experiments. The calculations are also in agreement with recent observations on an artificial aurora produced in the atmosphere with 8.7-keV electrons.

Evaluation of the collision stopping power of elements and compounds for electrons and positrons

This paper gives tables of material properties needed for the evaluation of the collision stopping power for electrons and positrons according to the Bethe theory. The key quantity is the mean excitation energy of the medium, which has been derived for many materials by a critical analysis of experimental data. Also given are the density-effect parameters of the theory of Sternheimer and Peierls. The material properties are given for the elements and for 180 compounds and mixtures, and the rules are described by which they could be obtained for other materials. Tables are also given of auxiliary quantities which depend only on the kinetic energy of the incident electron. These, together with the main tables, make possible the quick-and-easy evaluation of the collision stopping power.

Response functions for sodium iodide scintillation detectors

Abstract The response of sodium iodide detectors to gamma rays has been calculated by a method that takes into account the multiple scattering and escape from the detector of the incident gamma rays as well as of the secondary charged particles and bremsstrahlung. The method is applicable to gamma rays with arbitrarily high energies, and its accuracy has been verified by comparisons with experimental response functions at energies up to 20 MeV. A systematic tabulation has been made of the response functions for 3″ x 3″ detectors irradiated with broad parallel beams of gamma rays, at energies between 100 keV and 20 MeV. These results are given in a parametrized form which makes it easy to interpolate with respect to incident gamma-ray energy. A few response functions have also been calculated for detectors irradiated with 50 MeV gamma rays. Exploratory calculations have shown that 3″ x 3″ detectors are “omnidirectional” in the sense that the shape of the response function depends very little on the direction of the incident gamma-ray beam. Therefore, the tabulated data for broad parallel beams incident perpendicularly can, in good approximation, also be applied to other source geometries, e.g. the case of a detector exposed to an isotropic gamma-ray flux.

Penetration and Diffusion of X Rays

In the early period of X-ray research, the radiation sources were discharge tubes with applied potentials well below 100 key. X rays from these sources interact with matter primarily through the photoelectric effect. Their penetration is then limited by photoelectric absorption and is adequately described by an exponential law.

Some new results on electron transport in the atmosphere

Abstract The penetration, diffusion and slowing down of electrons in a semi-infinite air medium has been studied by the Monte Carlo method. The results are applicable in the atmosphere at altitudes up to ~ 300 km. Most of the results pertain to monoenergetic electron beams, with energies between 2 keV and 2 MeV, injected into the atmosphere at a height of 300 km, either vertically downwards or with a pitch-angle distribution isotropic over the downward hemisphere. Some results were also obtained for various initial pitch angles between 0° and 90°. Information has been generated concerning the following topics: 1. (a) the backscattering of electrons from the atmosphere, expressed in terms of backscattering coefficients, angular distributions and energy spectra; 2. (b) the altitude dependence of energy deposition by electrons and by secondary bremsstrahlung, for incident electron beams that are monoenergetic or have exponential spectra with e-folding energies between 5 and 200 keV; 3. (c) the evolution of electron flux spectra as function of the atmospheric depth, for incident beam energies between 2 and 20 keV.

Bremsstrahlung in the atmosphere.

Calculations are described pertaining to the emission of bremsstrahlung by electrons in the upper atmosphere and the penetration of this radiation to atmospheric depths of 3–10 g cm−2 where it can be measured by balloon-borne detectors. The calculations take into account the multiple scattering and slowing down of electrons, and the multiple Compton scattering and photoelectric absorption of bremsstrahlung photons. Numerical data have been generated for electron beams incident onto the atmosphere with energies between 20 keV and 2 MeV, assuming wide-area precipitation and an incident angular distribution isotropic over the downward hemisphere. The results relate the number and energy spectrum of the incident electrons to the bremsstrahlung flux spectrum at balloon heights. The interpretation of some observed bremsstrahlung flux spectra is attempted.