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Il Nuovo Cimento (1955-1965)

, Volume 6, Issue 3, pp 614–627 | Cite as

Theory of high-energy potential scattering

  • D. S. Saxon
  • L. I. Schiff
Article

Summary

A new formulation for high-energy potential scattering, presented in a recent paper, is extended to provide explicit formulas for the scattering theory of the three-dimensional non-separable Schrödinger equation. An integral equation is derived, for which a single iteration gives the scattering when the potential energy is not too large and is slowlyvarying compared to a wavelength. The result agrees with those obtained earlier for small and for large scattering angles, but applies as well to intermediate angles and improves the earlier accuracy. Further iterations can provide greater accuracy as well as an error estimate for the first approximation.

Riassunto

Si estende una nuova formulazione dello scattering per potenziali di alta energia presentata in un recente lavoro, per ricavare formole esplicite per la teoria dello scattering dell’equazione tridimensionale non, separabile di Schrödinger. Si deriva un’equazione integrale per la quale una sola iterazione dà lo scattering se l’energia potenziale non è troppo grande e varia lentamente rispetto a una lunghezza d’onda. Il risultato si accorda con quelli ottenuti precedentemente per angoli di scattering piccoli e grandi, ma si puÒ altrettanto bene applicare agli angoli medi e migliora la precedente esattezza. Ulteriori iterazioni possono dare maggior esattezza, come pure una stima dell’errore della prima approssimazione.

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References

  1. (1).
    L. I. Schiff:Phys. Rev.,103, 443 (1956).MathSciNetADSCrossRefGoogle Scholar
  2. (2).
    D. S. Saxon:Formulation of High Energy Potential Scattering Problems (submitted for publication to thePhys. Rev.).Google Scholar
  3. (3).
    The analysis of the remainder of this section is a slight extension of that of’E. Feenberg:Plys. Rev.,40, 40 (1932), andL. I. Schiff:Progr. Theor. Phys. (Kyoto),.11, 288 (1954).ADSCrossRefMATHGoogle Scholar
  4. (4).
    R. Glauber andV. Schomaker:Phys. Rev.,89, 667 (1953).ADSCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1957

Authors and Affiliations

  • D. S. Saxon
    • 1
    • 3
  • L. I. Schiff
    • 2
    • 4
  1. 1.Universitetets Institut for Teoretisk FysikCopenhagen
  2. 2.Laboratoire de Physique, école Nonnale SupérieureUniversité de ParisFrance
  3. 3.University of CaliforniaLos AngelesUSA
  4. 4.Stanford UniversityStanfordUSA

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