Practical Ranges of Electrons and Positrons in Intermediate and High Energy Region for Condensed Materials

Author Affiliations

  • 1Department of Physics, B. S. A. College, Mathura, India, 281004
  • 2Department of Physics, B. S. A. College, Mathura, India, 281004

Res. J. Physical Sci., Volume 4, Issue (9), Pages 1-6, November,4 (2016)

Abstract

The present paper presents a simple empirical formula for the practical ranges of electrons and positrons from atomic numbers 1 to 92 in different materials. The formula is existing in the expression of the multiplication of factor related to the continuous-slowing-down approximation (CSDA) range and to multiple scattering detours. The factor being articulated as a parameter of electron energy received by the target (incident) and atomic number of the medium (Z). For CSDA range in the practical-range formula, exact recorded values available or an fairly accurate methodical expression derived as a parameter of electron energy received by the target (incident) and atomic number of the medium, atomic weight and mean excitation energy of medium can be used. The utmost variation of the consequential formula with the other accessible data was 2%. The formula can also be applied to not too heavy compounds and mixtures by using an effectual atomic number and atomic weight. It is quite clear from the results drawn that this method gives better concurrence with the existing data.

References

  1. Tabata T., Ito R., Okabe S. and Fujita Y. (1971)., Projected-Range Straggling of 4-to 24-MeV Electrons in Elemental Materials., Japanese Journal of Applied Physics, 10(11), 1503.
  2. Tabata T., Andreo P., Shinoda K. and Ito R. (1995)., Depth profiles of charge deposition by electrons in elemental absorbers: Monte Carlo results, experimental benchmarks and derived parameters. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms., 95(3), 289-299.
  3. Sorcini B.B., Andreo P., Bielajew A.F., Hyodynmaa S. and Brahme A. (1995)., An improved energy-range relationship for high-energy electron beams based on multiple accurate experimental and Monte Carlo data sets., Physics in medicine and biology, 40(7), 1135.
  4. Fernández-Varea J.M., Andreo P. and Tabata T. (1996)., Detour factors in water and plastic phantoms and their use for range and depth scaling in electron-beam dosimetry., Physics in medicine and biology, 41(7), 1119.
  5. Tabata T., Ito R. and Okabe S. (1972)., Generalized semiempirical equations for the extrapolated range of electrons., Nuclear Instruments and Methods, 103(1), 85-91.
  6. Tabata T. and Ito R. (1975)., A generalized empirical equation for the transmission coefficient of electrons., Nuclear Instruments and Methods,127(3), 429-434.
  7. Tabata T. and Ito R. (1974)., An algorithm for the energy deposition by fast electrons., Nuclear Science and Engineering, 53(2), 226-239.
  8. Halbleib J.A., Kensek R.P., Valdez G.D., Seltzer S.M. and Berger M.J. (1992)., ITS: the integrated TIGER series of electron/photon transport codes-Version 3.0., IEEE Transactions on Nuclear Science, 39(4), 1025-1030.
  9. Halbleib J.A., Kensek R.P., Mehlhorn T.A., Valdez G.D., Seltzer S.M. and Berger M.J. (1992)., ITS version 3.0: the integrated TIGER series of coupled electron/photon Monte Carlo transport codes., SAND 91-1634.
  10. Tabata T., Ito R., Okabe S. and Fujita Y. (1971)., Extrapolated and Projected Ranges of 4‐to 24‐MeV Electrons in Elemental Materials., Journal of Applied Physics, 42(9), 3361-3366.
  11. Weber K.H. (1963)., Eine einfache reichweite-energie-beziehung für elektronen im energiebereich von 3 keV bis 3 MeV., Nuclear Instruments and Methods, 25, 261-264.
  12. Vzorov I.K. (1969)., Range-Energy Relation for High Energy Electron Beams., Joint Inst. Nucl. Res., (Dubna) Report JINR-P1-4529.
  13. Burrell M.O. and Watts Jr, J.W. (1971)., Electron and bremsstrahlung penetration and dose calculation., NASA-TN-D-6385, M-440.
  14. Ito R., Tabata T. and Okabe S. (1971)., Function Fitting to the Range-Energy Relation of Electrons., Annu. Rep. Radiat. Center Osaka Prefect, 12, 49-53 (1971).
  15. Mukoyama T. (1976)., Range of electrons and positrons., Nuclear Instruments and Methods, 134(1), 125-127.
  16. Matthews M.D. (1980)., A simple method for the approximate calculation of electron ranges in media., Radiation Effects, 51(3-4), 209-213.
  17. Gupta S.K. and Gupta D.K. (1980)., An Empirical Equation for the csda Range Difference of 0.2-to 10-MeV Electrons., Japanese Journal of Applied Physics, 19(1), 1-3.
  18. Gupta S.K. and Gupta D.K. (1981)., Continuous slowing‐down approximation range of 50‐keV–100‐MeV electrons., Journal of Applied Physics, 52(3), 1175-1178.
  19. Gol, Approximation of electron range as a function of their energy and a substance atomic number., Atomnaya Ehnergiya, 52(2), 134.
  20. Tabata T., Andreo P. and Shinoda K. (1996)., An analytic formula for the extrapolated range of electrons in condensed materials., Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 119(4), 463-470.
  21. Saxena Anshu, Rathi S.K., Verma Ajay Singh (2011)., Continuous Slowing down Approximation (CSDA) ranges of electrons for biomedical materials., Elixir Bio. Phys., 37, 3860-3863
  22. Berger M.J. and Seltzer S.M. (1964)., Tables of energy losses and ranges of electrons and positrons., NASA SP-3012. NASA Special Publication, 3012.
  23. Rathi S.K. (1982)., Penetration of Electrons and Positrons through different materials., Department of Physics, Aligarh Muslim University, Aligarh.
  24. Newhauser W. (2009)., International Commission on Radiation Units and Measurements Report 78: Prescribing, Recording and Reporting Proton-beam Therapy., Radiation Protection Dosimetry.