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Matrix Padé Approximants for the S01 and P03 Partial Waves in Nucleon-Nucleon Scattering

J. Fleischer, J. L. Gammel, and M. T. Menzel

  • Department of Physics, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544

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Phys. Rev. D 8, 1545 – Published 1 September, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.1545

Abstract

In order to correct the threshold behavior of scalar Padé approximants in NN scattering, "matrix Padé approximants," which take into account the various positive- and negative-energy states, have been considered by several authors. In a recent paper by Bessis, Turchetti, and Wortman, truncated matrices based on an incomplete set of basis states were used and a qualitative description of the energy dependence of the P03 phase shift was obtained. In this work it is shown that this result is not obtained when a complete set of basis states is used. The main effect of matrix Padé approximants using a complete set of basis states is to introduce an additional attraction at higher energies. Our analysis of the fourth-order graphs is done in a way which allows the external momenta to be completely off shell so that the irreducible graphs can be used as kernels in the Bethe-Salpeter equation. This will make possible the calculation of several higher-order graphs by iterating the Bethe-Salpeter equation.

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Comments & Replies

Matrix Padé approximants and the Bethe-Salpeter equation of the N−N interaction

A. Gersten, D. A. Owen, J. L. Gammel, P. Mery, and G. Turchetti
Phys. Rev. D 13, 1140 (1976)

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Phys. Rev. D 8, 1545– Published 1 September, 1973
  • Received 23 April 1973

© 1973 American Physical Society

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