Pion Electromagnetic Form Factor from Coulomb Interference

Abstract

Using recent 24-MeV ${\pi }^{\pm }-\alpha$ elastic scattering data we critically analyze the Hofstadter-Sternheim proposal for measuring the pion electromagnetic form factor. A phenomenological nonlocal potential, whose parameters are fixed directly from the data, is used to describe the nuclear interaction. Using these parameters, a type of distorted-wave Born approximation is then employed to calculate the Coulomb contributions. We conclude that (i) nuclear distortion effects on the Coulomb contribution are large; (ii) the fits are not very sensitive to the pion radius and from the data only a conservative upper limit of ∼1.5 F can be reasonably given; (iii) experimental statistics need to be greatly improved before a more definitive result can be obtained; (iv) sensitivity to the model parameters seems to be smallest in the region of backward scattering (${\theta }_{\mathrm{lab}}\gtrsim 100°$), where sensitivity to the pion radius is greatest; and (v) the fruitfulness of going to much higher energies (>100 MeV) is probably quite limited. Some suggestions for present and future experimental and theoretical work are briefly discussed.