Off-shell πN amplitudes via a multichannel separable potential |
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Authors: | JT Londergan KW McVoy EJ Moniz |
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Institution: | 1. Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 USA;3. Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 USA |
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Abstract: | The off-shell pion-nucleon transition matrix is a basic ingredient in theories of pion-nuclear interactions which, in the absence of fundamental theory of πN dynamics, must be obtained by a phenomenological extrapolation from the available on-shell data. As one means of performing such an extrapolation, we explore a multichannel separable potential model with the property that the off-shell elastic scattering amplitude is generated directly from the measured elastic-channel phase shifts. The off-shell πN partial-wave transition amplitudes determined by this procedure are compared with those calculated by Landau and Tabakin using a one-channel absorptive separable potential. We find that the absorptive separable potential approach provides a physically unreasonable off-shell extrapolation at energies where the on-shell amplitude is highly inelastic, and show that the difficulty is a direct consequence of the one-channel nature of that method. The multichannel extrapolation is free of these difficulties. |
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