[en] The off-shell single-scattering impulse approximation is applied to medium-energy pion-alpha particle elastic scattering and to low energy electron--hydrogen molecule elastic and rotationally inelastic scattering. For the pion-alpha particle system, using a Gaussian nuclear wave function and a simple separable off-shell amplitude, results are obtained ranging from good agreement with experiment at 206 MeV/c to fair agreement at 85 MeV/c. Comparisons are made with various on-shell theories. For the electron--molecule problem, using a point-charge, rigid-rotor, harmonic-oscillator molecular wave function consisting of two point charges, with charge as an adjustable parameter, and the exact off-shell Coulomb amplitude, results are obtained that do not agree well with the available experimental data. Speculations are made concerning the results using more realistic charge distributions