Advertisement

Communications in Mathematical Physics

, Volume 101, Issue 2, pp 291–304 | Cite as

Truncation of continuum ambiguities in phase-shift analysis

  • D. Atkinson
  • I. S. Stefanescu
Article

Abstract

The continuum ambiguity in the determination of phase shifts from scattering data consists of a family of amplitudes which have in general an infinite number of partial waves. In practical computations, however, the partial wave series is necessarily truncated. We discuss the relation of the resulting (truncated) amplitudes to those representing the true continuum ambiguity. In particular, we show that each of the latter is approximated increasingly well, as the cut-off tends to infinity, uniformly inside an ellipse in the cosθ plane.

Keywords

Neural Network Statistical Physic Complex System Phase Shift Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atkinson, D., Mahoux, G., Yndurain, F.J.: Construction of a unitary analytic scattering amplitude (I). Scalar particles. Nucl. Phys. B54, 263 (1973)Google Scholar
  2. 2.
    Atkinson, D., Mahoux, G., Yndurain, F.J.: Construction of a unitary analytic scattering amplitude (II). Introduction of spin and isospin (spin 0-spin 1/2). Nucl. Phys. B66, 429 (1973)Google Scholar
  3. 3.
    Atkinson, D., Heemskerk, A.C., Swierstra, S.D.: Construction of a unitary scattering amplitude (V).π + p scattering. Nucl. Phys. B109, 322 (1976)Google Scholar
  4. 4.
    Atkinson, D., de Roo, M., Polman, T.: There is a continuum ambiguity for elasticπN amplitudes. Phys. Lett.148 B, 361 (1984)Google Scholar
  5. 5.
    Atkinson, D., Kaekebeke, M., de Roo, M.: Phase shifts as functions of the cross-section. J. Math. Phys.16, 685 (1975)Google Scholar
  6. 6.
    Kantorowich, L.W., Akilow, G.P.: Funktionalanalysis in normierten Räumen. Berlin: Akademie Verlag, 1964 (German translation of Russian original)Google Scholar
  7. 7.
    Cartan, H.: Calcul différentiel. Paris: Hermann 1967Google Scholar
  8. 8.
    Erdelyi, A.: ed.) Higher transcendental functions, Vol. II. New York: McGraw Hill 1953Google Scholar
  9. 9.
    Barrelet, E.: A new point of view in the analysis of two-body reactions. Nuovo Cimento8 A, 331 (1972)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • D. Atkinson
    • 1
  • I. S. Stefanescu
    • 2
  1. 1.CERNGeneva 23Switzerland
  2. 2.Institut für Theoretische KernphysikKarlsruheFederal Republic of Germany

Personalised recommendations