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Soft Collisions

  • Brian J. McParland
Chapter

Abstract

This chapter prevents a number of theories associated with soft collisions, that is, those interactions between a charged projectile and the entire atom (which Bohr referred to as nuclear collisions). We begin with applying our earlier analysis of projectile momentum and atomic electron screening in elastic scatter to a new analysis of the conditions of soft collisions. Then, the theory of soft-collision energy loss is developed using classical mechanics. First, the Rutherford formula is developed. This is followed by a thorough analysis of the Bohr theory from both classical and semi-classical points of view. As an aside, the Fermi model of soft-collision energy loss, which is based upon classical electrodynamic theory, is investigated not only on its own right but also for the foundations that it provides for the derivation of the Bethe quantum-mechanical theory of soft-collision energy loss and the effects of a condensed medium upon collision energy loss as discussed in  Chap. 12. Bethe’s theory is then developed. Initially, this is for the nonrelativistic regime and is then extended to relativistic energies.

Keywords

Energy Transfer Momentum Transfer Impact Parameter Differential Cross Section Dipole Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. Attix FH. Introduction to radiological physics and radiation dosimetry. New York: Wiley; 1986.Google Scholar
  2. Berger MJ, Seltzer SM. Stopping powers and ranges of electrons and positrons. NBSIR 82-2550-A. Washington, DC: National Bureau of Standards; 1983.Google Scholar
  3. Bjorken JD, Drell SD. Relativistic quantum mechanics. New York: McGraw-Hill; 1964.Google Scholar
  4. Bloch F. Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie. Ann Phys. 1933a;16:285–320.Google Scholar
  5. Brice DK, Sigmund P. Secondary electron spectrum from dielectric theory. Matt Fys Medd Dan Vid Selsk. 1980;40:1–34.Google Scholar
  6. Enz PC, editor. Pauli lectures on physics: vol 6. Selected topics on field quantization. Cambridge: Wolfgang Pauli. Massachusetts Institute of Technology; 1973.Google Scholar
  7. Gould RJ. Electromagnetic processes. Princeton: Princeton University Press; 2006.Google Scholar
  8. Green G. An essay on the application of mathematical analysis to the theories of electricity and magnetism; 1828.Google Scholar
  9. ICRU. Stopping powers and ranges for electrons and positrons. ICRU Report 37. Bethesda: International Commission on Radiation Units and Measurements; 1984.Google Scholar
  10. ICRU. Stopping powers and ranges for protons and alpha particles. ICRU Report 49. Bethesda: International Commission on Radiation Units and Measurements; 1993.Google Scholar
  11. Jordan EG, Balmain KG. Electromagnetic waves and radiating systems. Englewood Cliffs: Prentice Hall Inc; 1968.Google Scholar
  12. Ziegler JF. The stopping of energetic light ions in elemental matter. J Appl Phys. 1999;85:1249–72.Google Scholar

References

  1. Abramowitz M, Stegun IA, editors. Handbook of mathematical functions. New York: Dover Publications; 1972.Google Scholar
  2. Ahlen SP. Theoretical and experimental aspects of the energy loss of relativistic heavy ionizing particles. Rev Mod Phys. 1980;52:121–73 (erratum Rev Mod Phys 1980; 52: 653).CrossRefGoogle Scholar
  3. Anderson C, Neddermeyer S. New evidence for the existence of a particle intermediate between the proton and electron. Phys Rev. 1937;52:1003–4.CrossRefGoogle Scholar
  4. Bethe HA. Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie. Ann Phys. 1930;5:324–400.Google Scholar
  5. Bethe HA. Bremsformel für Elektronen relativisticher Geschwindigkeit. Z Physik. 1932;76:293–9.CrossRefGoogle Scholar
  6. Bloch F. Zur Bremsun rasch bewegter Telichen beim Durchgang durch Materie. Ann Physik. 1933;16:285–320.CrossRefGoogle Scholar
  7. Bohr N. On the theory of the decrease of velocity of moving electrified particles on passing through matter. Philos Mag. 1913;25:10–31.Google Scholar
  8. Bohr N. On the decrease of velocity of swiftly moving electrified particles in passing through matter. Philos Mag. 1915;30:581–612.Google Scholar
  9. Bohr N. The penetration of atomic particles through matter. Matt Fys Medd Dan Vild Selsk. 1948;18(8):1–144.Google Scholar
  10. Darwin CG. A theory of the absorption and scattering of the α rays. Philos Mag. 1912;23:901–21.Google Scholar
  11. Fano U. Penetration of protons, alpha particles and mesons. Annu Rev Nucl Sci. 1963;13:1–66.CrossRefGoogle Scholar
  12. Fermi E. The absorption of mesotrons in air and in condensed materials. Phys Rev. 1939;56:1242.CrossRefGoogle Scholar
  13. Fermi E. The ionization loss of energy in gases and in condensed materials. Phys Rev. 1940;47:485–92.CrossRefGoogle Scholar
  14. Fernández-Vaera JM. Monte Carlo simulation of the inelastic scattering of electrons and positrons using optical-data models. Rad Phys Chem. 1998;53:235–45.CrossRefGoogle Scholar
  15. Gaunt JA. The stopping power of hydrogen atoms of α-particles according to the new quantum theory. Proc Camb Philos Soc. 1927;23:732–54.CrossRefGoogle Scholar
  16. Henderson GH. The decrease in energy of α particles passing through matter. Philos Mag. 1922;44:680–8.Google Scholar
  17. Jackson JD. Classical electrodynamics. New York: Wiley; 1999.Google Scholar
  18. McParland BJ. Nuclear medicine radiation dosimetry: advanced theoretical principles. London: Springer; 2010.CrossRefGoogle Scholar
  19. Neufeld J. Electron capture and loss by moving ions in dense media. Phys Rev. 1954;96:1470–8.CrossRefGoogle Scholar
  20. Rossi B. High-energy particles. New York: Prentice-Hall; 1952.Google Scholar
  21. Segrè E. Nuclei and particles. 2nd ed. Reading: Benjamin/Cummings; 1977.Google Scholar
  22. Sigmund P. Low-velocity limit of Bohr’s stopping power formula. Phys Rev A. 1996;54:3113–17.PubMedCrossRefGoogle Scholar
  23. Sigmund P. Particle penetration and radiation effects. Berlin: Springer; 2006.Google Scholar
  24. Slater JC. Atomic radii in crystals. J Chem Phys. 1964;41:3199–204.CrossRefGoogle Scholar
  25. Thomson JJ. Ionization by moving electrified particles. Philos Mag. 1912;6–23:449.Google Scholar
  26. Thorsen J (ed). The penetration of charged particles through matter. In: Niels Bohr: collected works. Amsterdam: Elsevier NV; 1987.Google Scholar
  27. Uehling EA. Penetration of heavy charged particles in matter. Annu Rev Nucl Sci. 1954;4:315–50.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Brian J. McParland
    • 1
  1. 1.Amersham, BuckinghamshireUK

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