Pion-Deuteron Scattering in the Impulse Approximation

The pure-scattering model of Fernbach, Green, and Watson is used to obtain impulse approximation expressions for the elastic, elastic plus inelastic (closure approximation), and charge-exchange (closure approximation) $\pi -d$ differential cross sections. The net interference where $p$-wave scattering is dominant is found to be constructive; the interference due to charge exchange scattering is always negative. The Coulomb effect gives rise to strong destructive interference in the ${\pi }^{+}-d$ elastic component at 85 Mev (laboratory energy of incident pion) for angles $\frac{3}{2}, \frac{3}{2}$) double scattering indicates that Brueckner's model is unreliable at low energies. The binding correction to the impulse approximation is calculated using a $p$-state interaction Hamiltonian (PV coupling) and found to be -3.2 mb at 85 Mev. The forward peak in the elastic differential cross section is found appreciably reduced by destructive interference arising from elastic "absorptive" scattering. It is concluded that, at energies ≲100 Mev, absorption corrections are significant, with the multiple-scattering correction becoming important at higher energies.