Some corrections to partial wave dispersion relations for pion photoproduction
McKinley, John McKeen
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https://hdl.handle.net/2142/16653
Description
Title
Some corrections to partial wave dispersion relations for pion photoproduction
Author(s)
McKinley, John McKeen
Issue Date
1962
Doctoral Committee Chair(s)
Jackson, J.D.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
pion photoproduction
Language
en
Abstract
The exact one dimensional dispersion relations for partial wave amplitudes of pion-nucleon scattering and of pion photoproduction on nucleons were derived and compared. It was found that a non-constant comparison function must be introduced into the relationship between the scattering partial wave amplitude which is dominant at low energies and the corresponding photoproduction partial wave amplitude, in order that each amplitude obey its own exact dispersion relation at the same time that the two amplitudes are related by the unitarity condition.
The results of experimental determinations of pion-nucleon scattering phase shifts were compiled, and the coefficients of interpolation formulae for the phase shifts were evaluatedo Two sets of interpolation formulae were found, one of which attempts to incorporate all experiments while the other disregards three intermediate-energy experiments Which do not appear to follow the trend of the other experiments. The experimental results of photoproduction of neutral and of positive pions on protons at energies up to 500 Mev were compared to calculated cross sections for various combinations of choice of phase shifts and inclusion of the comparison function. There was no overwhelming indication either for or against the inclusion of the comparison function.
The photoproduction cross sections were also calculated with the inclusion of the contribution of the “bipion”. The effect of this contribution was generally greater than the effect of either the comparison function or a change of phase shifts. On the basis of the π+ angular distribution it appeared that the coupling parameter for this contribution should be negative.
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