Low-Energy Behavior of the Phase Shifts in Pion-Proton Scattering

Abstract

A best fit has been made to all pion-proton scattering phase-shift information under 80 Mev assuming the energy dependence of the phase shifts is momentum to the power ($2l+1$) which would be the case for strong short-range interactions. The values obtained for the Fermi-type solutions are ${\alpha }_{33}=0.235\mathrm{}{\eta }^3$, ${\alpha }_3=-0.11\mathrm{}\eta$, and ${\alpha }_1=0.16\mathrm{}\eta$. These phase shifts, along with Coulomb forces, fit all scattering experiment data quite closely including the 5-Mev cloud chamber results at Columbia. However, at zero energy they predict $({\alpha }_1-{\alpha }_3)=0.27\mathrm{}\eta$, while recent photoproduction results and the Panofsky effect as evaluated here predict $({\alpha }_1-{\alpha }_3)=0.21\mathrm{}\eta$ with rather large uncertainties.