Quantum Inverse Scattering Theory and Nucleon-Nucleon Potentials

  • Th. Kirst
  • H. Kohlhoff
  • H. V. von Geramb
Conference paper
Part of the Inverse Problems and Theoretical Imaging book series (IPTI)


The Gel’fand-Levitan and Marchenko quantum inverse scattering theory has been applied to construct nucleón nucleon (NN) potentials. Its aim was to use inversion theory as a mean to construct local and energy independent channel potentials from meson-theoretical predictions of phase shifts, or phase shift analyses results to NN data. Various derivations of the fundamental equations have been studied to facilitate calculations with existing data. A new integral equation has also been found which relates the Gel’fand-Levitan and Marchenko output kernels in a transparent way. For application, a most practical form of the theory is deduced by starting with a rational function representation of the phase shift data and by using Padé approximants for e z , therewith rational representations of the S-matrix, Jost functions and other useful quantities are determined. The excellent reproductive power was studied using both fundamental equations and with the Reid soft core potential and their phase shifts respectively. Serious results use the meson theoretical phase shifts from the Paris and the Bonn groups, and experimental phases from Arndt et al. Finally, half off-shell T-matrices were generated to compare the exact meson theoretical results with those of inversion and it is found that phase equivalent interactions have essentially the same off-shell behaviour for any physically significant range of momenta.


Nucleon Nucleon Output Kernel Phase Shift Function Meson Theory Inversion Potential 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Chadan and P.C. Sabatier, Inverse problems in quantum scattering theory, (Springer New York 1977, Second Edition 1989 ).Google Scholar
  2. [2]
    M. Lacombe, B. Loiseau, J.M. Richard, R. Vinh Mau, J. Cote, P. Pires and R. De Tourreil, Parametrization of the Paris Potential, Phys. Rev. C21, 861 (1980).Google Scholar
  3. [3]
    R. Machleidt, K. Holinde and CH. Elster, The Bonn meson-exchange model for the nucleon-nucleon interaction, Phys. Rep. 149 (1), (1987).Google Scholar
  4. [4]
    R.A. Arndt, J.S. Hyslop III and L.D. Roper, Nucleon-nucleon partial-wave analysis to 1100 MeV, Phys. Rev. D35 (l), 128 (1986). R.A. Arndt and L.D. Roper, Scattering Analysis Interactive Dial-in SAID, ( Virginia Polytechnic Institute, Blacksbury, 1988 ).Google Scholar
  5. [5]
    TH. Kirst, K. Amos, L. Berge, M. Coz and H.V. V. Geramb, Nucleón Nucleón Potentials from GePfand-Levitan and Marchenko Inversions, Phys. Rev. C40, 912 (1989).CrossRefGoogle Scholar
  6. [6]
    TH. Kirst, Nukleon Nukleon Potentiale aus der Inversion, PhD thesis, University of Hamburg (1989).Google Scholar
  7. [7]
    H. Kohlhoff, Rationale Darstellungen der Nukleon Nukleon S-Matrix, Diplomarbeit, University of Hamburg (1989).Google Scholar
  8. [8]
    H.V. V. Geramb and K. Amos Off-shell T-matrices from inverse scattering, submitted to Phys. Rev. C (9/1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Th. Kirst
  • H. Kohlhoff
  • H. V. von Geramb
    • 1
  1. 1.Theoretical Nuclear PhysicsUniversity of HamburgFed. Rep. of Germany

Personalised recommendations