Phase-Shift Optical Model Calculations for the Elastic Scattering of Pions on Aluminum

Phys. Rev. 100, 1431 – Published 1 December 1955
Aihud Pevsner and James Rainwater


Theoretical optical-model exact phase-shift calculations are given for the predicted elastic scattering of pions from aluminum at the energy used (79 Mev) in the experimental studies described in the preceding paper. The predicted curves show strong diffraction minima, not present in the experimental curves. We have emphasized a comparison of the results of these calculations with those of more approximate methods. Sixteen choices of constant complex potentials were used for r<R0 for both π+ and π- mesons, with a Coulomb potential for r>R0=3.600λ. Here k0=λ is the momentum at infinity and (k1+ik2) is the momentum for r<R0. It is found that the predicted incoherent cross section σa and positions of the diffraction minima depend strongly on k1k0 for a fixed k2. Values of σa>πR02 are obtained for relatively long nuclear mean free paths (2k2)-1 for incoherent processes for the attractive potentials which give best fit to experiment. The results of various modified Born approximation calculations are compared with the results of the exact calculations.


  • Received 31 March 1955
  • Published in the issue dated December 1955

© 1955 The American Physical Society

Authors & Affiliations

Aihud Pevsner* and James Rainwater

  • Department of Physics, Columbia University, New York, New York

  • *Now at the Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts.

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