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Coulomb corrections to low energy |N phase shifts Bankes, Stephen Alexander


In this thesis a phenomenology is given with the view to determining the electromagnetic contributions to the low energy πN S-wave phase shifts. The approach we take is to partition the Coulomb potential into a short and a long ranged part at some arbitrary cutoff radius. Subsequently we deduce expressions which allow us to estimate, in two distinct stages, first the short and then the long range electromagnetic modifications to the purely hadronic physical observable quantities. The analysis formally begins with a discussion of the single channel π+p—> π+p elastic scattering process. We then turn our attention to the two channel process π⁻p—> π⁻p, π°n. Although a more complete discussion of π⁻p low energy scattering should necessarily entail the inclusion of the third channel inelastic process π⁻p—> ƴn, we have chosen to ignore this in order that we may elucidate some of the ambiguities that have existed with the two channel analysis. Explicit calculations are done, for the energy range 11.6 Mev ≤ T[sub= π][sup= LAB] ≤ 44.0 Mev. For input we use energy dependent expressions for the hadronic phase shifts. Although our estimates to the Coulomb modifications to these quantities do display the same general features with those found in the literature, the numbers we get for the π⁻p phase shifts are considerably smaller. This we attribute to our omission of the ƴn channel. The encouraging feature we do find however is that the procedure developed for treating both the one and the two channel problems are nearly identical. The only difference is that the latter necessitates the use of the unitarity constraint on the scattering matrix. This we hope will serve as a useful guide for a future discussion of the three channel problem.

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