Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 107, Issue 12, pp 2767–2772 | Cite as

Simple local potential for the spectrum of e+ e coincidence peaks found in heavy-ion collisions

  • T. A. Weber
  • C. L. Hammer
Article

Summary

Recent observations of narrow positron-electron coincidence peaks in heavy-ion collisions have raised renewed interest in discrete bound states embedded in the continuum first proposed by Wigner and von Neumann. In this paper we present a simple local potential which supports multiple bound states with energies that match the coincidence peaks. These positive-energy bound states have no classical turning points. Since the results are derived by analytical methods, this potential provides a simple test of numerical procedures used to study such phenomena.

PACS

25.70.Ef - Resonances 

PACS

03.65.Ge - Solutions of wave equations: bound states 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T Cowan et al.:Phys. Rev. Lett.,56, 444 (1986);T. Cowan andJ. S. Greenberg: inPhysical of Strong Fields, edited byW. Greiner (Plenum Press, New York, N.Y., 1987), p. 111;P. Salabura et al.:Phys. Lett. B,245, 153 (1990).CrossRefADSGoogle Scholar
  2. [2]
    W. Koenig et al.:Phys. Lett. B,218, 12 (1989).CrossRefADSGoogle Scholar
  3. [3]
    J. R. Spence andJ. P. Vary:Phys. Lett. B,254, 1 (1990);J. P. Vary et al.:Recent Progress in Many-Body Theories, Vol.3, edited byT. L. Ainsworth et al. (Plenum Press, New York, N.Y., 1992), p. 93.CrossRefADSGoogle Scholar
  4. [4]
    J. von Neumann andE. Wigner:Z. Phys.,30, 465 (1929).Google Scholar
  5. [5]
    F. H. Stillinger andD. R. Herrick:Phys. Rev. A,11, 446 (1975).CrossRefADSGoogle Scholar
  6. [6]
    See, for example,J. Mathews andR. L. Walker:Mathematical Method of Physics, 2nd edition (W. A. Benjamin, New York, N.Y., 1970), pp. 198–204.Google Scholar
  7. [7]
    E. Merzbacker:Quantum Mechanics, 2nd edition (John Wiley and Sons, New York, N.Y., 1970), pp. 93–105.Google Scholar
  8. [8]
    E. P. Wigner:Phys. Rev.,46, 1002 (1934);Trans. Faraday Soc.,34, 678 (1938).CrossRefADSGoogle Scholar
  9. [9]
    C. M. Care andN. H. March:Adv. Phys.,24, 101 (1975).CrossRefADSGoogle Scholar
  10. [10]
    A. W. Overhauser:Phys. Rev. Lett.,4, 415, 462 (1960).CrossRefADSMATHGoogle Scholar
  11. [11]
    F. Capasso et al.:Nature,358, 565 (1992).CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1994

Authors and Affiliations

  • T. A. Weber
    • 1
  • C. L. Hammer
    • 1
  1. 1.Department of Physics and AstronomyIowa State UniversityAmesUSA

Personalised recommendations