Bremsstrahlung Cross Section Research Articles

Absolute cross sections of ultra-soft x-ray radiation in electron scattering upon atoms and the soft-photons approximation

We calculated the cross sections of ultra-soft x-ray bremsstrahlung in electron scattering upon Ar, Kr and Xe. The results are consistent with the absolute values of the differential cross sections measured by Gnatchenko et al. (2009) [17] for scattering electrons with an energy of 600 eV on these atoms.

Bremsstrahlung of 5–25-keV electron impact with Al, Cu, Ag, Te, and Au thick solid targets with no polarization contribution

Bremsstrahlung spectra generated by electrons with incident energies of 5--25 keV bombarding thick targets of $\mathrm{Al}\phantom{\rule{0.16em}{0ex}}(Z=13), \mathrm{Cu}\phantom{\rule{0.16em}{0ex}}(Z=29), \mathrm{Ag}\phantom{\rule{0.16em}{0ex}}(Z=47), \mathrm{Te}\phantom{\rule{0.16em}{0ex}}(Z=52)$, and $\mathrm{Au}\phantom{\rule{0.16em}{0ex}}(Z=79)$ are measured with high accuracy. Comparing the experimental spectra with the simulated spectra obtained from the Monte Carlo code penelope, it is found that they are in excellent agreement. The penelope code contains only the cross sections for ordinary bremsstrahlung, while disregarding polarization bremsstrahlung. The results quite definitely indicate that there is no polarization bremsstrahlung contribution to the x-ray radiation spectra produced by incident electrons with thick solid targets for the x-ray energies of interest in this paper ($g1\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$).

The DSM theory for tip electron-atom bremsstrahlung at [formula omitted] MeV

The Dirac–Sommerfeld-Maue (DSM) theory for electron bremsstrahlung at the short-wavelength limit, based on a point-Coulomb description of the target nucleus, is tested against the Dirac partial-wave (DW) theory at collision energies up to 35 MeV. It is found that for the small photon angles, which contribute to the angle-integrated bremsstrahlung yield, the screening effects are at most in the percent region. Predictions are made for the nuclear charge dependence of the singly differential bremsstrahlung cross section at 500 MeV, where experiments are planned in the near future.

Analytic calculations of electron–nucleus bremsstrahlung cross sections above a few MeV including higher-order corrections and multiple scattering in the target

Calculations of the elementary process of electron–nucleus bremsstrahlung employing a partial–wave expansion of the initial and final electron wave functions are exact and offer results that match the experimental data, but they become impractical for increasingly higher electron energies, especially in some regions of the emitted photon phase space. Here we take the opposite approach and use analytic expressions based on the Olsen–Maximon–Wergeland additivity rule, valid above few MeV, to decouple the calculation of the screening and Coulomb corrections. The former is obtained from the first Born approximation, while the latter is evaluated within the formalism of the Furry–Sommerfeld–Maue wave functions using the leading–order expression by Elwert and Haug and the next–to–leading–order corrections by Roche, Ducos, and Proriol, which is presently the best way to calculate cross sections for electrons with energies in the range of hundreds of MeV. A detailed discussion of the approximations involved and an extensive comparison with experimental data have been published in previous works. Here we focus on the numerical procedures that have been developed and on the stringent cross checks that have been performed to ensure the accuracy of the results. Published benchmark calculations for bremsstrahlung in a pure Coulomb field, that stop at 100 keV, are extended here to 100 MeV by making available selected values that could be used by other independent researchers to validate their programs. We also discuss the numerical details of the procedure adopted to convolve the bremsstrahlung cross section with the impinging electron angular distribution due to multiple scattering in the target.

On higher–order corrections to nuclear bremsstrahlung cross sections

A quantitative understanding of bremsstrahlung by electrons in the screened field of atomic nuclei has been developed by several researchers over the last 80 years. However, some ranges of the possible parameters can still not be covered with good accuracy. Dirac partial-wave calculations are the best method developed to date, while analytic calculations are the only viable solution at high impinging electron energies. Recent progresses on both fronts will be discussed. In particular, state of the art partial wave results, including screening, allowed to test the Olsen–Maximon–Wergeland additivity rule discovered by analytic means. Closed expressions for the next-to-leading order corrections to the Furry–Sommerfeld–Maue wave functions are known. One next-to-next-to-leading order term is typically included in this type of approach. The effect of this extra term on the angular dependence of the double differential cross sections for photon emission by 2.5 MeV electrons is compared in detail with partial wave calculations which are exact at all orders.

Shape functions and singly differential cross sections of bremsstrahlung at electron energies from 10 eV to 3 MeV for Z[formula omitted] 1–100

This work describes a library of shape functions and singly differential cross sections of bremsstrahlung due to interaction of the electrons with energies from 10 eV to 3 MeV with neutral atoms. The calculations have been performed using an updated version of the set of codes BREMS, which was described in a previous publication. The calculation method is based on the relativistic partial-wave formulation describing interaction of the incident electron with a central potential of the neutral target atom. The interaction potential is obtained from the Kohn–Sham density functional theory. The Dirac equation for the continuum wave function is solved by the power-series method. The mentioned library uses a comparatively dense grid of the incident electron energy (ten points per decade), and it covers all chemical elements with atomic numbers from 1 to 100. The agreement of the present data with the previously-published tabulations is satisfactory.

LPM effect in cosmic-ray electron observations with emulsion chambers

We have performed a series of cosmic-ray electron + positron observations using balloon-borne emulsion chambers since 1968, together with electron beam tests at CERN-SPS. In emulsion chamber experiments, we can measure the location of shower tracks in each emulsion plate with a precision of 1 μm. Because of the high position resolution, we can identify the first electron-positron pairs of electron-induced showers. The LPM effect predicts a reduction of amplitude for bremsstrahlung photon emission by a high-energy electron. It causes the optical depth of the first electron-positron pair to increase. From the measurements of the first pair depths with 200 GeV and 250 GeV beam electrons at CERN, and cosmic ray electrons + positrons from 400 GeV to 3 TeV (on average at 900 GeV), we found direct evidence of suppression of the bremsstrahlung cross section due to the LPM effect. In this work, we present the experimental results compared to analytic approximations and Monte-Carlo simulations.

Empirical formula for bremsstrahlung cross-section in actinides

We have formulated the empirical formula for bremsstrahlung cross section in actinides. This formula produces bremsstrahlung cross sections for electrons with energies from 1 keV to 10 GeV incident on atoms with atomic numbers Z = 89 to 103. This formula produces bremsstrahlung cross sections with simple inputs of energy of incident electron (T), energy of emitted bremsstrahlung photon and atomic number of the target.

Empirical formula for bremsstrahlung cross-section in actinides

We have formulated the empirical formula for bremsstrahlung cross section in actinides. This formula produces bremsstrahlung cross sections for electrons with energies from 1 keV to 10 GeV incident on atoms with atomic numbers Z = 89 to 103. This formula produces bremsstrahlung cross sections with simple inputs of energy of incident electron (T), energy of emitted bremsstrahlung photon and atomic number of the target.

Electron–atom bremsstrahlung cross sections in the 20–100 keV energy region: absolute measurements for and comparison with theoretical databases

We report absolute measurements of doubly differential electron–atom bremsstrahlung cross sections for energies in the keV region and elements with atomic numbers 6, 13, 52, 73 and 79. Thin targets were irradiated at the low-energy beam line of the São Paulo Microtron with 20, 50, 75 and 100 keV electrons. For each element and energy, the photon spectra were collected simultaneously with three HPGe detectors at the emission angles of 35°, 90° and 131°. The deconvolution of the bremsstrahlung spectra was done adopting an analytical model for the spectrometers’ response functions. The resulting doubly differential cross sections are compared with the available partial-wave calculations of ordinary bremsstrahlung. Based on this comparison, we discuss some features of the experimental spectra that might be related to the emission of polarization bremsstrahlung.

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.

Bremsstrahlung shielding parameters in polymer concretes

ABSTRACTConcretes are used for shielding in nuclear power plants. Beta radiation is emitted during the nuclear reactions. This beta radiation interacts with the concrete and results in secondary radiation such as bremsstrahlung. Shielding parameters of beta-induced bremsstrahlung in concretes are important in the field of radiation protection. We have evaluated the cross section, yield, intensity and dose rate of beta-induced bremsstrahlung by pure beta nuclides of end point energy ranges from 0.4 to 5 MeV in some polymer-based concretes such as sulfur polymer concrete, barium polymer concrete, calcium polymer concrete, fluorine polymer concrete, chlorine polymer concrete and germanium polymer concrete. We have compared the shielding properties among the studied polymer concretes. The efficiency, intensity and dose rate of bremsstrahlung increases with a maximum energy of beta nuclide and modified atomic number of the concrete. From the detailed study, it is clear that the barium polymer concrete is having large bremsstrahlung dose rate and specific bremsstrahlung constant values than the other studied polymer concretes. This means barium polymer concrete is a good absorber of bremsstrahlung radiation than the other studied polymer concretes.

The [formula omitted] beam line of the São Paulo Microtron electron accelerator

The São Paulo Microtron 10−100keV electron beam-line described here was designed to allow precise measurements of the electron-atom interaction cross-sections using reproducible arrangements. The irradiation chamber has thirteen spectroscopy windows for x-ray detectors and a multi-target ladder. The photon background on the target was reduced by using a large and deep Faraday cup, lining the chamber's interior with plastic, and mounting the targets in carbon fiber frames. The current research plan includes measurements of: electron doubly differential bremsstrahlung cross sections; inner shell ionization cross sections; angular distributions of L X-rays, and the angular distribution of scattered electrons.

Bremsstrahlung from few-electron ions

We have developed the new approach which can be used for accurate evaluations of the bremsstrahlung cross-sections in the case of few-electron atoms and ions. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. Multiple bremsstrahlung from few-electron ions is considered. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma.

Diffractive bremsstrahlung at high-beta ^star LHC

Feasibility studies of the measurement of the exclusive diffractive bremsstrahlung cross-section in proton–proton scattering at the centre of mass energy of 13 TeV at the LHC are reported. Present studies were performed for the low luminosity LHC running with the betatron function value of 90 m using the ATLAS associated forward detectors ALFA and ZDC. A simplified approach to the event simulation and reconstruction is used. The background influence is also discussed.

Higher-order corrections to electron-nucleus bremsstrahlung cross sections above a few MeV

Higher-order corrections to electron-nucleus bremsstrahlung cross sections above a few MeV

Sci‐Thur PM – Brachytherapy 01: Fast brachytherapy dose calculations: Characterization of egs_brachy features to enhance simulation efficiency

Purpose:egs_brachy is a fast, new EGSnrc user‐code for brachytherapy applications. This study characterizes egs_brachy features that enhance simulation efficiency.Methods:Calculations are performed to characterize efficiency gains from various features. Simulations include radionuclide and miniature x‐ray tube sources in water phantoms and idealized prostate, breast, and eye plaque treatments. Features characterized include voxel indexing of sources to reduce boundary checks during radiation transport, scoring collision kerma via tracklength estimator, recycling photons emitted from sources, and using phase space data to initiate simulations. Bremsstrahlung cross section enhancement (BCSE), uniform bremsstrahlung splitting (UBS), and Russian Roulette (RR) are considered for electronic brachytherapy.Results:Efficiency is enhanced by a factor of up to 300 using tracklength versus interaction scoring of collision kerma and by up to 2.7 and 2.6 using phase space sources and particle recycling respectively compared to simulations in which particles are initiated within sources. On a single 2.5 GHz Intel Xeon E5‐2680 processor cor, simulations approximating prostate and breast permanent implant ((2 mm)3 voxels) and eye plaque ((1 mm)3) treatments take as little as 9 s (prostate, eye) and up to 31 s (breast) to achieve 2% statistical uncertainty on doses within the PTV. For electronic brachytherapy, BCSE, UBS, and RR enhance efficiency by a factor >2000 compared to a factor of >104 using a phase space source.Conclusion:egs_brachy features provide substantial efficiency gains, resulting in calculation times sufficiently fast for full Monte Carlo simulations for routine brachytherapy treatment planning.

Parametric interference effect in nonresonant spontaneous bremsstrahlung of an electron in the field of a nucleus and two pulsed laser waves

Nonresonant spontaneous bremsstrahlung of an electron scattered by a nucleus in the field of two moderately strong pulsed waves is studied theoretically. The process is studied in detail within the interference kinematic region. This region is determined by scattering of particles in the same plane at predetermined angles, at which stimulated absorption and emission of photons of external pulsed waves by an electron occur in a correlated manner. It is shown that the probability of the partial process with correlated emission (absorption) by an electron of the equal number of photons of the both waves is of an order of the magnitude greater than the corresponding probability in any other scattering kinematics. The cross section of spontaneous bremsstrahlung in two pulsed waves may be two times greater than the cross section of a free-field process after summation over all stimulated processes of correlated emission and absorption. Obtained results may be experimentally verified, for example, by scientific facilities at sources of pulsed laser radiation (SLAC, FAIR, ELI, XCELS).

TU-AB-BRC-08: Egs_brachy, a Fast and Versatile Monte Carlo Code for Brachytherapy Applications

Purpose: To introduce egs_brachy, a new, fast, and versatile Monte Carlo code for brachytherapy applications. Methods: egs_brachy is an EGSnrc user-code based on the EGSnrc C++ class library (egs++). Complex phantom, applicator, and source model geometries are built using the egs++ geometry module. egs_brachy uses a tracklength estimator to score collision kerma in voxels. Interaction, spectrum, energy fluence, and phase space scoring are also implemented. Phase space sources and particle recycling may be used to improve simulation efficiency. HDR treatments (e.g. stepping source through dwell positions) can be simulated. Standard brachytherapy seeds, as well as electron and miniature x-ray tube sources are fully modelled. Variance reduction techniques for electron source simulations are implemented (Bremsstrahlung cross section enhancement, uniform Bremsstrahlung splitting, and Russian Roulette). TG-43 parameters of seeds are computed and compared to published values. Example simulations of various treatments are carried out on a single 2.5 GHz Intel Xeon E5-2680 v3 processor core. Results: TG-43 parameters calculated with egs_brachy show excellent agreement with published values. Using a phase space source, 2% average statistical uncertainty in the PTV ((2mm)3 voxels) can be achieved in 10 s for 100 125I or 103Pd seeds in a 36.2 cm3 prostate PTV, 31 s for 64 103Pd seeds in a 64 cm3 breast PTV, and 56 s for a miniature x-ray tube in a 27 cm3 breast PTV. Comparable uncertainty is reached in 12 s in a (1 mm)3 water voxel 5 mm away from a COMS 16mm eye plaque with 13 103Pd seeds. Conclusion: The accuracy of egs_brachy has been demonstrated through benchmarking calculations. Calculation times are sufficiently fast to allow full MC simulations for routine treatment planning for diverse brachytherapy treatments (LDR, HDR, miniature x-ray tube). egs_brachy will be available as free and open-source software to the medical physics research community. This work is partially funded by the Canada Research Chairs program, the Natural Sciences and Engineering Research Council of Canada, and the Ontario Ministry of Research and Innovation (Ontario Early Researcher Award).

Rotational character of the12Cspectrum investigated through inelastic cross sections via photon emission

In this work the bremsstrahlung and photon dissociation cross sections for transitions between 0+ , 2+ , and 4+ states in 12 C are computed. The nucleus is described within the three-alpha model, and the wave functions are computed by means of the hyperspherical adiabatic expansion method. The continuum states are discretized by imposing a box boundary condition. The transition strengths are obtained from the cross sections, and compared to schematic rotational model predictions. The computed results strongly suggest that the two lowest bands are made, respectively, by the states with angular momentum and parity {01 + , 21 + , 42 + } and {02 + , 22 + , 41 + }. The transitions between the states in the first band are consistent with the rotational pattern corresponding to three alphas in an equilateral triangular structure. For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned distribution.