GitHub
[1]
E. E. Lewis and W. F. Miller. Computational methods of neutron transport (John Wiley and Sons, Inc., New York, NY, 1984).
[2]
A. Hébert. Applied reactor physics (Presses inter Polytechnique, 2009).
[3]
L. Lorence Jr, J. Morel and G. Valdez. Physics guide to CEPXS: a multigroup coupled electron-photon cross-section generating code (Sandia National Lab.(SNL-NM), Albuquerque, NM (United States), 1989).
[4]
J. Morel. Fokker-Planck calculations using standard discrete ordinates transport codes. Nuclear Science and Engineering 79, 340–356 (1981).
[5]
G. Pomraning. The Fokker-Planck operator as an asymptotic limit. Mathematical Models and Methods in Applied Sciences 2, 21–36 (1992).
[6]
S. B. Uilkema. Proton therapy planning using the SN method with the Fokker–Planck approximation. Delft University of Technology (2012).
[7]
G. Pomraning. Higher order fokker-planck operators. Nuclear science and engineering 124, 390–397 (1996).
[8]
E. Olbrant and M. Frank. Generalized Fokker–Planck theory for electron and photon transport in biological tissues: application to radiotherapy. Computational and mathematical methods in medicine 11, 313–339 (2010).
[9]
K. Przybylski and J. Ligou. Numerical analysis of the Boltzmann equation including Fokker-Planck terms. Nuclear Science and Engineering 81, 92–109 (1982).
[10]
Y. Azmy, E. Sartori, E. W. Larsen and J. E. Morel. Advances in discrete-ordinates methodology. Nuclear computational science: A century in review, 1–84 (2010).
[11]
J. S. Hesthaven and T. Warburton. Nodal discontinuous Galerkin methods: algorithms, analysis, and applications (Springer Science & Business Media, 2007).
[12]
F. Salvat, J. M. Fernández-Varea, J. Sempau and others. PENELOPE-2006: A code system for Monte Carlo simulation of electron and photon transport. In: Workshop proceedings, Vol. 4 (Citeseer, 2006); p. 7.
[13]
J. H. Hubbell, W. J. Veigele, E. Briggs, R. Brown, D. Cromer and d. R. Howerton. Atomic form factors, incoherent scattering functions, and photon scattering cross sections. Journal of physical and chemical reference data 4, 471–538 (1975).
[14]
D. T. Cromer. Anomalous dispersion corrections computed from self-consistent field relativistic Dirac–Slater wave functions. Acta Crystallographica 18, 17–23 (1965).
[15]
L. Kissel, B. Zhou, S. Roy, S. Sen Gupta and R. Pratt. The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in elastic scattering calculations. Acta Crystallographica Section A: Foundations of Crystallography 51, 271–288 (1995).
[16]
O. Iwamoto, N. Iwamoto, S. Kunieda, F. Minato, S. Nakayama, Y. Abe, K. Tsubakihara, S. Okumura, C. Ishizuka, T. Yoshida and others. Japanese evaluated nuclear data library version 5: JENDL-5, journal of nuclear science and technology 60, 1–60 (2023).
[17]
D. E. Cullen, M. Chen, J. Hubbell, S. Perkins, E. Plechaty, J. Rathkopf and J. Scofield. Tables and graphs of photon-interaction cross sections from 10 eV to 100 GeV derived from the LLNL evaluated photon data library (EPDL) (Lawrence Livermore National Lab., CA (USA), 1989).
[18]
D. Brusa, G. Stutz, J. Riveros, J. Fernández-Varea and F. Salvat. Fast sampling algorithm for the simulation of photon Compton scattering. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 379, 167–175 (1996).
[19]
W. Heitler. The quantum theory of radiation (Courier Corporation, 1984).
[20]
D. E. Cullen, J. H. Hubbell and L. Kissel. EPDL97: the evaluated photo data library97 version (Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States), 1997).
[21]
F. Sauter. Über den atomaren Photoeffekt in der K-Schale nach der relativistischen Wellenmechanik Diracs. Annalen der Physik 403, 454–488 (1931).
[22]
J. Baró, M. Roteta, J. Fernández-Varea and F. Salvat. Analytical cross sections for Monte Carlo simulation of photon transport. Radiation physics and chemistry 44, 531–552 (1994).
[23]
Y.-S. Tsai. Pair production and bremsstrahlung of charged leptons. Reviews of Modern Physics 46, 815 (1974).
[24]
H. Davies, H. Bethe and L. Maximon. Theory of bremsstrahlung and pair production. II. Integral cross section for pair production. Physical Review 93, 788 (1954).
[25]
I. Kawrakow and D. Rogers. The EGSnrc code system. NRC Report PIRS-701, NRC, Ottawa (2021).
[26]
J. M. Fernández-Varea, F. Salvat, M. Dingfelder and D. Liljequist. A relativistic optical-data model for inelastic scattering of electrons and positrons in condensed matter. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 229, 187–218 (2005).
[27]
C. Møller. Zur theorie des durchgangs schneller elektronen durch materie. Annalen der Physik 406, 531–585 (1932).
[28]
H. Bhabha. The scattering of positrons by electrons with exchange on Dirac’s theory of the positron. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences 154, 195–206 (1936).
[29]
S. M. Seltzer. Cross sections for bremsstrahlung production and electron-impact ionization. In: Monte Carlo transport of electrons and photons (Springer, 1988); pp. 81–114.
[30]
S. Perkins and D. Cullen. The Livermore electron impact ionization data base (Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States), 1989).
[31]
F. Salvat and J. Fernández-Varea. Semiempirical cross sections for the simulation of the energy loss of electrons and positrons in matter. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 63, 255–269 (1992).
[32]
F. Salvat. Bethe stopping-power formula and its corrections. Physical Review A 106, 032809 (2022).
[33]
F. Salvat, L. Barjuan and P. Andreo. Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections. Physical Review A 105, 042813 (2022).
[34]
J. H. Scofield. K-and L-shell ionization of atoms by relativistic electrons. Physical Review A 18, 963 (1978).
[35]
F. Salvat and J. M. Fernández-Varea. Overview of physical interaction models for photon and electron transport used in Monte Carlo codes. Metrologia 46, S112 (2009).
[36]
S. Perkins. Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL), Z = 1-100 (Lawrence Livermore National Laboratory, 1991).
[37]
F. Salvat and P. Andreo. SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula. Computer Physics Communications 287, 108697 (2023).
[38]
S. M. Seltzer and M. J. Berger. Evaluation of the collision stopping power of elements and compounds for electrons and positrons. The International Journal of Applied Radiation and Isotopes 33, 1189–1218 (1982).
[39]
S. Seltzer, J. Fernandez-Varea, P. Andreo, P. Bergstrom, D. Burns, I. Krajcar Bronić, C. Ross and F. Salvat. Key data for ionizing-radiation dosimetry: measurement standards and applications, ICRU Report 90 (ICRU, 2016).
[40]
F. Rohrlich and B. Carlson. Positron-electron differences in energy loss and multiple scattering. Physical review 93, 38 (1954).
[41]
U. Fano. Atomic theory of electromagnetic interactions in dense materials. Physical Review 103, 1202 (1956).
[42]
M. Inokuti and D. Y. Smith. Fermi density effect on the stopping power of metallic aluminum. Physical Review B 25, 61 (1982).
[43]
R. M. Sternheimer. The density effect for the ionization loss in various materials. Physical Review 88, 851 (1952).
[44]
T. Lijian, H. Qing and L. Zhengming. Analytic fitting to the Mott cross section of electrons. Radiation Physics and Chemistry 45, 235–245 (1995).
[45]
M. Boschini, C. Consolandi, M. Gervasi, S. Giani, D. Grandi, V. Ivanchenko, P. Nieminem, S. Pensotti, P. Rancoita and M. Tacconi. An expression for the Mott cross section of electrons and positrons on nuclei with Z up to 118. Radiation Physics and Chemistry 90, 39–66 (2013).
[46]
I. Kawrakow. Improved modeling of multiple scattering in the voxel Monte Carlo model. Medical physics 24, 505–517 (1997).
[47]
S. M. Seltzer. An overview of ETRAN Monte Carlo methods. Monte Carlo transport of electrons and photons, 153–181 (1988).
[48]
G. Moliere. Theorie der streuung schneller geladener teilchen i. einzelstreuung am abgeschirmten coulomb-feld. Zeitschrift für Naturforschung A 2, 133–145 (1947).
[49]
U. Fano. Inelastic collisions and the Moliere theory of multiple scattering. Physical Review 93, 117 (1954).
[50]
X. A. Li and D. Rogers. Electron mass scattering powers: Monte Carlo and analytical calculations. Medical Physics 22, 531–541 (1995).
[51]
W. Koepf. Hypergeometric summation. Vieweg, Braunschweig/Wiesbaden 5 (1998).
[52]
I. S. Gradshteyn and I. M. Ryzhik. Table of integrals, series, and products (Academic press, 2014).
[53]
M. Landesman and J. Morel. Angular Fokker-Planck decomposition and representation techniques. Nuclear Science and Engineering 103, 1–11 (1989).
[54]
J. Morel. On the validity of the extended transport cross-section correction for low-energy electron transport. Nuclear Science and Engineering 71, 64–71 (1979).
[55]
C. R. Drumm, W. C. Fan, L. Lorence and J. Liscum-Powell. An analysis of the extended-transport correction with application to electron beam transport. Nuclear science and engineering 155, 355–366 (2007).
[56]
J. E. Morel. A hybrid collocation-Galerkin-Sn method for solving the Boltzmann transport equation. Nuclear Science and Engineering 101, 72–87 (1989).
[57]
S. M. Seltzer and M. J. Berger. 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. Atomic data and nuclear data tables 35, 345–418 (1986).
[58]
E. Acosta, X. Llovet and F. Salvat. Monte Carlo simulation of bremsstrahlung emission by electrons. Applied Physics Letters 80, 3228–3230 (2002).
[59]
L. Kissel, C. Quarles and R. Pratt. Shape functions for atomic-field bremsstrahlung from electrons of kinetic energy 1–500 keV on selected neutral atoms 1 $\le$ Z $\le$ 92. Atomic data and nuclear data tables 28, 381–460 (1983).
[60]
L. Kim, R. Pratt, S. Seltzer and M. Berger. Ratio of positron to electron bremsstrahlung energy loss: an approximate scaling law. Physical Review A 33, 3002 (1986).
[61]
F. Salvat, J. Fernández-Varea, J. Sempau and X. Llovet. Monte Carlo simulation of bremsstrahlung emission by electrons. Radiation Physics and Chemistry 75, 1201–1219 (2006).
[62]
A. Poškus. Shape functions and singly differential cross sections of bremsstrahlung at electron energies from 10 eV to 3 MeV for Z= 1–100. Atomic Data and Nuclear Data Tables 129, 101277 (2019).
[63]
W. R. Nelson, H. Hirayama and D. W. Rogers. EGS4 code system (Stanford Linear Accelerator Center, Menlo Park, CA (USA), 1985).
[64]
G. Collaboration and others. Physics reference manual (CERN, Switzerland, 2016).
[65]
A. Naceur, C. Bienvenue, P. Romano, C. Chilian and J.-F. Carrier. Extending deterministic transport capabilities for very-high and ultra-high energy electron beams. Scientific Reports 14, 2796 (2024).
[66]
A. Hébert and A. Naceur. Implementation of the ELECTR module in NJOY. In: EPJ Web of Conferences, Vol. 284 (EDP Sciences, 2023); p. 11001.
[67]
A. Elbert and A. Laforgia. An inequality for Legendre polynomials. Journal of Mathematical Physics 35, 1348–1360 (1994).
[68]
C. Bienvenue and A. Hébert. High-order diamond differencing schemes for the Boltzmann Fokker–Planck equation in 1D and 2D Cartesian geometries. Annals of Nuclear Energy 171, 109032 (2022).
[69]
G. B. Arfken, H. J. Weber and F. E. Harris. Mathematical methods for physicists: a comprehensive guide (Academic press, 2011).
[70]
F. G. Tricomi. Sugli zeri dei polinomi sferici ed ultrasferici. Annali di Matematica Pura ed Applicata 31, 93–97 (1950).
[71]
N. Hale and A. Townsend. Fast and accurate computation of Gauss–Legendre and Gauss–Jacobi quadrature nodes and weights. SIAM Journal on Scientific Computing 35, A652–A674 (2013).
[72]
B. G. Carlson. A method of characteristics and other improvements in solution methods for the transport equation. Nuclear science and engineering 61, 408–425 (1976).
[73]
J. Bezanson, A. Edelman, S. Karpinski and V. B. Shah. Julia: A fresh approach to numerical computing. SIAM review 59, 65–98 (2017).