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Multiple scattering of charged particles by N atoms

Charles J. Joachain1 and Niels J. Kylstra2,*

  • 1Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 227, 1050 Brussels, Belgium
  • 2Spectroscopy, Quantum Chemistry and Atmospheric Remote Sensing, Université Libre de Bruxelles, CP 160/09, 1050 Brussels, Belgium

  • *niels.kylstra@gmail.com
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Phys. Rev. A 107, 042804 – Published 7 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042804

Abstract

The scattering of charged particles by N atoms is investigated theoretically. We derive the scattering equations by applying the approach of Faddeev that was originally developed to study quantum mechanically the scattering of three particles. We focus on the case in which the distance between the N target atoms is sufficiently large to allow the interactions between the atoms to be neglected. The Faddeev equations can then be reduced to a linear system whose solution is valid from the low-energy diffusive scattering regime, where the Foldy-Lax approach is often applied, to the ballistic regime, where multiple-scattering effects are small. To illustrate the method, results of calculations of the scattering of electrons by random configurations of 250 atoms, modeled by spherical potential wells, are presented. As an additional application, the solution obtained by Mott for the inelastic scattering of α particles by two atoms is extended to N atoms.

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References (45)

  1. N. F. Mott, Proc. R. Soc. London A 126, 79 (1929).
  2. L. I. Schiff, Quantum Mechanics (McGraw Hill, New York, 1955), p. 209.
  3. A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1966), p. 848.
  4. L. L. Foldy, Phys. Rev. 67, 107 (1945).
  5. M. Lax, Rev. Mod. Phys. 23, 287 (1951); Phys. Rev. 85, 621 (1952).
  6. V. Twersky, J. Opt. Soc. Am. 52, 145 (1962).
  7. P. C. Waterman and R. Truell, J. Math. Phys. 2, 512 (1961).
  8. B. U. Felderhof and B. Cichocki, J. Stat. Phys. 55, 1157 (1989).
  9. J. Korringa, Physica 13, 392 (1947).
  10. W. Kohn and N. Rostoker, Phys. Rev. 94, 1111 (1954).
  11. J. S. Faulkner, G. M. Stocks, and Y. Wang, Multiple Scattering Theory: Electronic Structure of Solids (Institute of Physics, Bristol, 2018).
  12. P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
  13. W. Guerin, M. Rouabah, and R. Kaiser, J. Mod. Opt. 64, 895 (2017).
  14. F. Pinsker, Sci. Rep. 6, 20751 (2016).
  15. J. Richard, L.-K. Lim, V. Denechaud, V. V. Volchkov, B. Lecoutre, M. Mukhtar, F. Jendrzejewski, A. Aspect, A. Signoles, L. Sanchez-Palencia, and V. Josse, Phys. Rev. Lett. 122, 100403 (2019).
  16. M.-L. Xu, J. J. Barton, and M. A. Van Hove, Phys. Rev. B 39, 8275 (1989).
  17. F. J. García de Abajo, M. A. Van Hove, and C. S. Fadley, Phys. Rev. B 63, 075404 (2001).
  18. D. Eng and L. Erdös, Rev. Math. Phys. 17, 669 (2005).
  19. J. Griffin and J. Marklof, J. Stat. Phys. 184, 16 (2021).
  20. T. Binninger, V. N. Shatokhin, A. Buchleitner, and T. Wellens, Phys. Rev. A 100, 033816 (2019).
  21. K. E. Aidala, R. E. Parrott, T. Kramer, E. J. Heller, R. M. Westervelt, M. P. Hanson, and A. C. Gossard, Nat. Phys. 3, 464 (2007).
  22. K. M. Watson, Phys. Rev. 105, 1388 (1957).
  23. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), p. 749.
  24. D. Gaspard and J.-M. Sparenberg, Phys. Rev. A 105, 042204 (2022).
  25. D. Gaspard and J.-M. Sparenberg, Phys. Rev. A 105, 042205 (2022).
  26. L. D. Faddeev, Sov. Phys. JETP 12, 1014 (1961); Sov. Phys. Dokl. 6, 384 (1961); 7, 600 (1963).
  27. C. J. Joachain and C. Quigg, Rev. Mod. Phys. 46, 279 (1974).
  28. C. J. Joachain, Quantum Collision Theory, 3rd ed. (North Holland, Amsterdam, 1983).
  29. L. D. Faddeev and S. P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer, Dordrecht, 1993).
  30. C. Cacciapuoti, R. Carlone, and R. Figari, Rep. Math. Phys. 59, 337 (2007).
  31. R. Figari and A. Teta, Quantum Dynamics of a Particle in a Tracking Chamber, SpringerBriefs in Physics (Springer, Berlin, 2014).
  32. G. F. Dell'Antonio, Found. Phys. 45, 11 (2015).
  33. D. Gaspard and J.-M. Sparenberg, Int. J. Quantum Inf. 17, 1941004 (2019).
  34. D. Gaspard, Phys. Rev. A 106, 062211 (2022).
  35. D. A. Rowlands, J. B. Staunton, and B. L. Györffy, Phys. Rev. B 67, 115109 (2003).
  36. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, Cambridge, 2006).
  37. J. B. Pendry, Low Energy Electron Diffraction: The Theory and its Application to Determination of Surface Structure (Academic, London, 1974).
  38. C. Schwartz, Phys. Rev. 124, 1468 (1961).
  39. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt, Orlando, 1976).
  40. K. M. Watson, J. Math. Phys. 10, 688 (1969).
  41. M. B. Hastings, A. D. Stone, and H. U. Baranger, Phys. Rev. B 50, 8230 (1994).
  42. E. J. Heller, Phys. Rev. Lett. 77, 4122 (1996).
  43. S. Li and E. J. Heller, Phys. Rev. A 67, 032712 (2003).
  44. S. A. Morgan, M. D. Lee, and K. Burnett, Phys. Rev. A 65, 022706 (2002).
  45. T. Takemiya, Prog. Theor. Phys. 48, 1547 (1972).

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Phys. Rev. A 107, 042804– Published 7 April, 2023
  • Received 4 February 2023
  • Accepted 21 March 2023
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