Skip to main content

Part of the book series: Ettore Majorana International Science Series ((EMISS,volume 38))

Abstract

A series of Monte Carlo codes for the calculation of the transport of electrons and photons through extended media has been developed at the National Bureau of Standards over the past 25 years. These codes have been named ETRAN (for Electron TRANsport), with the various versions representing mainly refinements, embellishments and different geometrical treatments that share the same basic algorithms for simulating by random sampling the course of electrons and photons as they travel through matter. These algorithms, which taken together have been called the ETRAN model, form the basis also of codes written at other laboratories, such as Sandia’s older SANDYL code and their more current series of the TIGER, CYLTRAN, and ACCEPT codes described elsewhere in this volume. In this chapter, the ETRAN methods are described as they are currently being implemented in our codes at NBS.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. J. Berger, “Monte Carlo Calculation of the Penetration and Diffusion of Fast Charged Particles”, in Methods in Computational Physics, Vol. 1, edited by B. Alder, S. Fernbach and M. Rotenberg, ( Academic Press, New York, 1963 ) 135.

    Google Scholar 

  2. J. H. Hubbell, “Photon Mass Attenuation and Energy-Absorption Coefficients from 1 keV to 20 MeV”, Int. J. Appl. Radiat. Isot. 33 (1982) 1269, and references therein.

    Google Scholar 

  3. J. H. Hubbell, M. J. Berger and S. M. Seltzer, “X-ray and Gamma-ray Cross Sections and Attenuation Coefficients”, National Bureau of Standards Standard Reference Database 8 (1985).

    Google Scholar 

  4. U. Fano, L. V. Spencer and M. J. Berger, “Penetration and Diffusion of X-Rays”, in Encyclopedia of Physics, Vol. 38/2, edited by S. Flügge, ( Springer, Berlin, 1959 ) 660.

    Google Scholar 

  5. O. Klein and Y. Nishina, “Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac”, Z. Phys. 52 (1929) 853.

    Article  ADS  MATH  Google Scholar 

  6. J. F. Williamson, F. C. Diebel and R. L. Morin, “The Significance of Electron- Binding Corrections in Monte Carlo Photon Transport Calculations”, Phys. Med. Biol. 29 (1984) 1063.

    Article  Google Scholar 

  7. H. A Bethe and J. Ashkin, “Passage of Radiations through Matter”, in Experimental Nuclear Physics, Vol. I, edited by E. Segre, ( John Wiley, New York, 1953 ) 166.

    Google Scholar 

  8. F. Fischer, “Beiträge zur Theorie der Absorption von Röntgenstrahlung”, Ann. Physik 8 (1931) 821.

    Article  ADS  Google Scholar 

  9. F. Sauter, “Über den atomaren Photoeffekt bei grosser Härte der anregenden Strahlung”, Ann. Physik 9 (1931) 217.

    Article  ADS  Google Scholar 

  10. S. M. Seltzer, “Calculated Response of Intrinsic Germanium Detectors to Narrow Beams of Photons with Energies up to ~ 300 keV”, Nucl. Instr. Meth. 188 (1981) 133.

    Article  Google Scholar 

  11. S. Goudsmit and J. L. Saunderson, “Multiple Scattering of Electrons”, Phys. Rev. 57 (1940) 24.

    Article  ADS  MATH  Google Scholar 

  12. G. Molière, “Theorie der Streuung schneller geladener Teilchen II: Mehrfach- und Vielfachstreuung”, Z. Naturforsch. 3a (1948) 78.

    ADS  Google Scholar 

  13. L. V. Spencer, “Theory of Electron Penetration”, Phys. Rev. 98 (1955) 1597.

    Article  ADS  MATH  Google Scholar 

  14. N. F. Mott, “The Scattering of Fast Electrons by Atomic Nuclei”, Proc. Roy. Soc. (London) A124 (1929) 425; see also J. A. Doggett and L. V. Spencer, “Elastic Scattering of Electrons and Positrons by Point Nuclei”, Phys. Rev. 103 (1956) 1597.

    ADS  Google Scholar 

  15. E. Rutherford, “The Scattering of αand ßParticles by Matter and the Structure of the Atom”, Philos. Mag. 21 (1911) 669.

    Article  MATH  Google Scholar 

  16. G. Molière, “Theorie der Streuung schneller geladener Teilchen I: Einzelstreuung am abgeschirmten Coulomb-Feld”, Z. Naturforsch. 2a (1947) 133.

    ADS  Google Scholar 

  17. E. Zeitler and H. Olsen, “Screening Effects in Elastic Electron Scattering”, Phys. Rev. A136 (1964) 1546.

    Article  ADS  Google Scholar 

  18. M. E. Riley, “Relativistic, Elastic Electron Scattering from Atoms at Energies Greater Than 1 keV”, Sandia National Laboratories report SLA-74–0107 (1974); and M. E. Riley, C. J. MacCallum and F. Biggs, “Theoretical Electron-Atom Elastic Scattering Cross Sections. Selected Elements, 1 keV to 256 keV”, Atom. Data and Nucl. Data Tables 15 (1975) 443.

    Article  ADS  Google Scholar 

  19. R. Wang, M. J. Berger and S. M. Seltzer, “Calculations of Electron Multiple Scattering”, Bull. Amer. Phys. Soc. 32 (1987) 765; see also Chapter 2 of this volume.

    Google Scholar 

  20. H. A. Bethe, “Molière’s Theory of Multiple Scattering”, Phys. Rev. 89 (1953) 1256.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. L. Landau, “On the Energy Loss of Fast Particles by Ionization”, J. Phys. (USSR) 8 (1944) 201.

    Google Scholar 

  22. M. S. Livingston and H. A. Bethe, “Nuclear Physics. C. Nuclear Dynamics, Experimental”, Rev. Mod. Phys. 9 (1937) 282.

    Article  Google Scholar 

  23. N. Bohr, “On the Decrease of Velocity of Swiftly Moving Electrified Particles in Passing through Matter”, Philos. Mag. 30 (1915) 581.

    Article  Google Scholar 

  24. E. J. Williams, “The Straggling of ß-Particles”, Proc. Roy. Soc. (London) 125 (1929) 420.

    Article  ADS  Google Scholar 

  25. C. Møller, “Zur Theorie des Durchgang schneller Elektronen durch Materie”, Ann. Physik. 14 (1932) 568.

    Google Scholar 

  26. H. J. Bhabha, “The Scattering of Positrons by Electrons with Exchange on Dirac’s Theory of the Positron”, Proc. Roy. Soc. (London) A154 (1936) 195.

    Article  ADS  Google Scholar 

  27. W. Börsch-Supan, “On the Evaluation of the Function $$\theta (\lambda ) = \int_{\sigma - i\infty }^{\sigma + i\infty } {{e^{\mu \ln \mu + \lambda \mu }}d\mu }$$for Real Values of λ ”, J. Res. National Bureau of Standards, 65B (1961) 245.

    Article  Google Scholar 

  28. O. Blunck and S. Leisegang, “Zum Energieverlust schneller Elektronen in dünnen Schichten”, Z. Physik 128 (1950) 500.

    Article  ADS  Google Scholar 

  29. O. Blunck and K. Westphal, “Zum Energieverlust energiereicher Elektronen in dünnen Schichten”, Z. Physik 130 (1951) 641.

    Article  ADS  Google Scholar 

  30. V. A. Chechin and V. C. Ermilova, “The Ionization-Loss Distribution at Very Small Absorber Thickness”, Nucl. Instr. Meth. 136 (1976) 551.

    Article  Google Scholar 

  31. J. Ph. Perez, J. Sevely and B. Jouffrey, “Straggling of Fast Electrons in Aluminum Foils Observed in High-Voltage Electron Microscopy (0.3–1.2 MV)”, Phys. Rev. A 16 (1977) 1061.

    Article  ADS  Google Scholar 

  32. W. Paul and H. Reich, “Energieverlust schneller Elektronen in Be, C, H2O, Fe und Pb”, Z. Physik 127 (1950) 429.

    Article  ADS  Google Scholar 

  33. G. Knop, A. Minton and B. Nellen, “Der Energieverlust von 1 MeV- Elektronen in sehr dünnen Schichten”, Z. Physik 165 (1961) 533.

    Article  ADS  Google Scholar 

  34. D. W. Aitken, W. L. Lakin and H. R. Zulliger, “Energy Loss and Straggling in Silicon by High-Energy Electrons, Positive Pions, and Protons”, Phys. Rev. 179 (1969) 393.

    Article  ADS  Google Scholar 

  35. K. Nagata, T. Doke, J. Kikuchi, N. Hasebe and A. Nakamoto, “Energy Loss and Straggling of High-Energy Electrons in Silicon Detectors”, Jap. J. Appl. Phys. 14 (1975) 697.

    Article  ADS  Google Scholar 

  36. W. Ogle, P. Goldstone, C. Gruhn and C. Maggiore, “Ionization Energy Loss of Relativistic Electrons in Thin Silicon Detectors”, Phys. Rev. Lett. 40 (1978) 1242.

    Article  ADS  Google Scholar 

  37. S. P. Moeller, private communication to H. Bichsel (1982), as reported in Reference 42.

    Google Scholar 

  38. S. Hancock, F. James, J. Movchet, P. G. Rancoita and L. VanRossum, “Energy Loss and Energy Straggling of Protons and Pions in the Momentum Range 0.7 to 115 GeV/c”, Phys. Rev. A 28 (1983) 615.

    Article  ADS  Google Scholar 

  39. D. West, “Measurement of the Energy Loss Distribution for Minimum Ionizing Electrons in a Proportional Counter”, Proc. Phys. Soc. (London) A 66 (1953) 306.

    Article  ADS  Google Scholar 

  40. F. Harris, T. Katsura, S. Parker, V. Z. Peterson, R. W. Ellsworth, G. B. Yodh, W. W. M. Allison, C. B. Brooks, J. H. Cobb and J. H. Mulvey, “The Experimental Identification of Individual Particles by the Observation of Transition Radiation in the X-Ray Region”, Nucl. Instr. Meth. 107 (1973) 413.

    Article  Google Scholar 

  41. N. Hasebe, J. Kikuchi, T. Doke, K. Nagata and A. Nakamoto, “Energy Loss of Relativistic Electrons and Its Fluctuation in Gas Proportional Counters”, Nucl. Instr. Meth. 155 (1978) 491.

    Article  Google Scholar 

  42. H. Bichsel, “Energy Loss and Ionization Spectra of Fast Charged Particles Traversing Thin Silicon Detectors”, submitted to Rev. Mod. Phys.

    Google Scholar 

  43. D. W. O. Rogers and A. F. Bielajew, “Differences in Electron Depth-Dose Curves Calculated with EGS and ETRAN and Improved Energy-Range Relationships”, Med. Phys. 13 (1986) 687.

    Article  Google Scholar 

  44. M. J. Berger and S. M. Seltzer, “Stopping Powers and Ranges of Electrons and Positrons (2nd Ed.)”, National Bureau of Standards report NBSIR 82-2550-A (1983); see also “Stopping Powers for Electrons and Positrons”, International Commission on Radiation Units and Measurements (ICRU) Report 37 (1984).

    Google Scholar 

  45. S. M. Seltzer and M. J. Berger, “Bremsstrahlung Spectra from Electron Interactions with Screened Atomic Nuclei and Orbital Electrons”, Nucl. Instr. Meth. B12 (1985) 95; and “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 ”, Atom. Data and Nucl. Data Tables 35 (1986) 345.

    Article  ADS  Google Scholar 

  46. See, e.g., W. Koch and J. W. Motz, “Bremsstrahlung Cross-Section Formulas and Related Data”, Rev. Mod. Phys. 31 (1959) 920.

    Article  ADS  Google Scholar 

  47. R. H. Pratt, H. K. Tseng, C. M. Lee, L. Kissel, C. MacCallum and M. Riley, “Bremsstrahlung Energy Spectra from Electrons of Kinetic Energy 1 keV ≤ T≤ 2000 keV Incident on Neutral Atoms 2 Z 92”, Atom. Data and Nucl. Data Tables 20 (1977) 175; errata in 26 (1981) 477.

    Article  ADS  Google Scholar 

  48. H. Davies, H. A. Bethe and L. C. Maximon, “Theory of Bremsstrahlung and Pair Production. II. Integral Cross Section for Pair Production”, Phys. Rev. 93 (1954) 788; and H. Olsen, “Outgoing and Ingoing Waves in Final States and Bremsstrahlung”, Phys. Rev. 99 (1955) 1335.

    Article  Google Scholar 

  49. E. Haug, “Bremsstrahlung and Pair Production in the Field of Free Electrons”, Z. Naturforsch. 30a (1975) 1099.

    ADS  Google Scholar 

  50. H. Kolbenstvedt, “Simple Theory for K-Ionization by Relativistic Electrons”, J. Appl. Phys. 38 (1967) 4785.

    Article  ADS  Google Scholar 

  51. A. M. Arthurs and B. L. Moisewitsch, “The K-Shell Ionization of Atoms by High-Energy Electrons”, Proc. Roy. Soc. (London) A247 (1958) 550.

    Article  ADS  Google Scholar 

  52. L. V. Spencer, “Energy Dissipation by Fast Electrons”, National Bureau of Standards Monograph 1 (1959).

    Google Scholar 

  53. S. M. Seltzer and M. J. Berger, “Electron and Photon Transport in Multi-Layer Media: Notes on the Monte Carlo Code ZTRAN”, National Bureau of Standards report NBSIR 84-2931 (1984); see also Int. J. Appl. Radiat. Isot. 38 (1987) 349.

    Article  Google Scholar 

  54. J. J. Dongarra, “Performance of Various Computers Using Standard Linear Equations Software in a FORTRAN Environment”, Argonne National Laboratory report TM 23 (1986).

    Google Scholar 

  55. J. H. Scofield, “Theoretical Photoionization Cross Sections from 1 to 1500 keV”, Lawrence Livermore National Laboratory Report UCRL-51326 (1973).

    Google Scholar 

  56. L. Kissel, C. A. Quarles and R. H. Pratt, “Shape Functions for Atomic-Field Bremsstrahlung from Electrons of Kinetic Energy 1-500 keV on Selected Neutral Atoms 1≤ Z ≤92”, Atom. Data and Nucl. Data Tables 28 (1983) 381.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Plenum Press, New York

About this chapter

Cite this chapter

Seltzer, S.M. (1988). An Overview of ETRAN Monte Carlo Methods. In: Jenkins, T.M., Nelson, W.R., Rindi, A. (eds) Monte Carlo Transport of Electrons and Photons. Ettore Majorana International Science Series, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1059-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-1059-4_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8314-0

  • Online ISBN: 978-1-4613-1059-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics