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Ion Screening in Solids

  • Werner Brandt

Abstract

In 1950, Hall [1] reported the results of an investigation of charge states in proton beams emerging from metals with energies between 20 and 400 keV, as summarized in Fig. 1.

Keywords

Proton Beam Annihilation Rate Density Enhancement Target Electron Projectile Velocity 
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.

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References

  1. [1]
    T. Hall, Phys. Rev. 79, 504 (1950).ADSCrossRefGoogle Scholar
  2. [2]
    K. O. Groeneveld and M. Kaminsky, Argonne National Laboratory Annual Report N. 7728, p. 177 (1969) and preprint.Google Scholar
  3. [3]
    H. Betz, Revs. Mod. Phys. 44, 465 (1972).ADSCrossRefGoogle Scholar
  4. [4]
    M. D. Brown and C. D. Moak, Phys. Rev. B 6, 90 (1972).ADSCrossRefGoogle Scholar
  5. [5]
    The constant rs can be calculated from the atomic weight of the target, A(g), its specific gravity d(g/cm3), and the number of valence electrons per target atom, N2, as rs = 1.389 (A/N2)1/3 a.u. Correspondingly, ρ0 = 8.92 x 10-2 (N2d/A) a.u. = 0.602 x 10 (N2d/A)cm-3. The electron gas has. in atomic units, the Fermi momentum \({k_{F}} = {(3{\pi ^{2}}{\rho _{O}})^{{1/3}}} = {(9\pi /4)^{{1/3}}}{r_{s}}^{{ - 1}} = 1.917{r_{s}}^{{ - 1}} \simeq 2{r_{s}}^{{ - 1}} \); the Fermi velocity becomes \({V_{F}} = {k_{F}} = 2{r_{s}}^{{ - 1}} \), the Fermi energy \({E_{F}} = {v_{F}}^{{2/2}} = 2r{{}_{s}^{{ - 2}}} \) and the plasma frequency \({\omega _{p}} = {(4\pi {\rho _{O}})^{{1/2}}} = {3^{{1/2}}}{r_{s}} - 3/2 \).Google Scholar
  6. [6]
    J. S. Langer and S. H. Vosko, J. Phys. Chem. Solids, 12, 196 (1959).ADSCrossRefGoogle Scholar
  7. [7]
    J. Friedel, Nuovo Cimento, Suppl. 2, 287 (1958).Google Scholar
  8. [8]
    H. Payne, Phys. Rev. B 1, 3645 (1970).ADSCrossRefGoogle Scholar
  9. [9]
    J. Friedel, Advanc. Phys. 3, 446 (1954).ADSCrossRefGoogle Scholar
  10. [10]
    P. Gombás, Die statistische Theorie des Atoms und ihre Anwendungen (Springer-Verlag, Wien 1949).MATHGoogle Scholar
  11. [11]
    E. H. Lieb and B. Siman, Phys. Rev. Lett. 31, 681 (1973).ADSCrossRefGoogle Scholar
  12. [12]
    N. F. Mott, Proc. Cambridge Phil. Soc. 32, 281 (1936).ADSMATHCrossRefGoogle Scholar
  13. [13]
    W. Brandt and J. Reinheimer, Can. J. Phys. 46, 607 (1968);ADSCrossRefGoogle Scholar
  14. [13a]
    W. Brandt and J. Reinheimer, Phys. Rev. B 2, 3104 (1970);ADSCrossRefGoogle Scholar
  15. [13n\b]
    W. Brandt and J. Reinheimer, Phys. Lett. 35A, 109 (1971).ADSGoogle Scholar
  16. [14]
    F. J. Rogers, H. C. Graboske, Jr., and D. J. Harwood, Phys. Rev. A 1, 1577 (1970); and references cited therein.ADSCrossRefGoogle Scholar
  17. [15]
    I. Isenberg, Phys. Rev. 79, 736 (1950).MathSciNetADSCrossRefGoogle Scholar
  18. [16]
    J. Callaway, Phys. Rev. 116, 1140 (1959).ADSCrossRefGoogle Scholar
  19. [17]
    J. Friedel, Phil. Mag. 43, 153 (1952).MATHGoogle Scholar
  20. [18]
    P. Bhattacharyya and K. S. Singwi, Phys. Rev. Lett. 29, 22 (1972).ADSCrossRefGoogle Scholar
  21. [19]
    J. Lindhard and A. Winther, Nuclear Phys. A166, 413 (1971).ADSGoogle Scholar
  22. [20]
    M. Ebel (private communication). We are grateful to Professor Ebel for the permission to show his results in Fig. 10 prior to publication.Google Scholar
  23. [21]
    O. B. Firsov, Zh. Eksp. Teor. Fiz [Sov. Phys. — JETP 36, 1076 (1959)];Google Scholar
  24. [21a]
    J. Lindhard, M. Scharff and H. E. Schiøtt, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 33, No. 14 (1963).Google Scholar
  25. [22]
    W. Whaling, “Handbuch der Physik,” edited by S. Flügge (Springer-Verlag, Berlin 1958) Vol. 34, p. 193 ff.Google Scholar
  26. [23]
    W. Brandt, J. Lindhard and M. Scharff, “Proc. Conf. Electronic and Atomic Collisions,” Boulder, Colorado (1961).Google Scholar
  27. [24]
    W. Brandt, Trans. New York Acad. Sci. 29, 210 (1966).CrossRefGoogle Scholar
  28. [25]
    W. Brandt and S. Lundqvist, Phys. Rev. A 139, A612 (1965).ADSGoogle Scholar
  29. [26]
    W. Brandt, L. Eder, and S. Lundqvist, J. Quant. Spectr. and Radiative Transfer 7, 411 (1967).ADSCrossRefGoogle Scholar
  30. [27]
    L. C. Northcliffe, Phys. Rev. 120, 1744 (1960).ADSCrossRefGoogle Scholar
  31. [28]
    H. W. Schnopper, H. D. Betz, J. P. Delvaille, K. Kalata, A. R. Sohval, K. W. Jones and H. E. Wegner, Phys. Rev. Lett. 29, 898 (1972).ADSCrossRefGoogle Scholar
  32. [29]
    F. Bell and H.-D. Betz; H. W. Schnopper (these Proceedings).Google Scholar
  33. [30]
    W. Brandt, R. Laubert, M. Mourino, and A. Schwarzschild, Phys. Rev. Lett. 30, 358 (1973).ADSCrossRefGoogle Scholar
  34. [31]
    J. Ashley, W. Brandt and R. H. Ritchie (these Proceedings) and papers cited therein; G. Basbas, W. Brandt, and R. Laubert, Phys. Lett. 34A, 277 (1971).ADSGoogle Scholar
  35. [32]
    N. Bohr and J. Lindhard, K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 28, 7 (1954).Google Scholar
  36. [33]
    H.-D. Betz and L. Brodzins, Phys. Rev. Lett. 25, 211 (1970).ADSCrossRefGoogle Scholar
  37. [34]
    W. Brandt and R. Sizmann, Phys. Lett. 37A, 115 (1971) and to be published.ADSGoogle Scholar
  38. [35]
    K. G. Harrison and M. W. Lucas, Phys. Lett. 33A, 142 (1970).ADSGoogle Scholar
  39. [36]
    J. Macek, Phys. Rev. A 1, 235 (1970).ADSCrossRefGoogle Scholar
  40. [37]
    A. Chateau-Thierry and A. Gladieux (these Proceedings).Google Scholar

Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • Werner Brandt
    • 1
  1. 1.Department of PhysicsNew York UniversityNew YorkUSA

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