Coulomb corrections to elastic pion-nucleus scattering in the eikonal model

Abstract

The Coulomb force modifies the elastic pion-nucleus scattering amplitude in impact parameter space in three distinct ways. There is an additive phase, a distortion of the pion's trajectory, and a shift in the effective energy of the pion-nucleus interaction. A formalism is derived for treating these effects when one has no microscopic scattering theory and the method is applied to $\text{π}{}^{\mathrm{\pm }}\text{−}{}^{12}\text{C}$ and $\text{π}{}^{\mathrm{\pm }}\text{−}{}^{40}\text{Ca}$ in the region of the first pion-nucleon resonance. The success of this amplitude analysis suggests that Coulomb corrections are understood well enough, at least at the higher energies, so that neutron distributions may be meaningfully investigated with pions.