Pion-Deuteron Elastic Scattering at 142 MeV and the Form-Factor Approximation

The differential cross section for charged pions with laboratory kinetic energy of 142 MeV to be scattered elastically by deuterons is calculated in a form-factor approximation which includes double scattering effects. The calculations also include effects produced by the $D$-state part of the deuteron wave function and the repulsive core in the neutron-proton interaction. A meson-theory derivation of an impulse- approximation series for the scattering amplitude using the Heitler-London method is described, as is an "optimal" procedure for obtaining a form-factor approximation to that series. The differences between the optimal form-factor approximation and other versions of the impulse approximation are discussed. The comparison of the calculations with experimental data indicates that pion-deuteron elastic scattering in the region of the first pion-nucleon resonance depends on off-energy-shell features of the pion-nucleon interaction which cannot be treated by a simple form-factor approximation.