The Interaction of a Charged Pi-Meson with the Deuteron

The radiative absorption, charge-exchange scattering, elastic and inelastic scattering of a ${\pi }^{+}$ meson by the deuteron are calculated in conventional weak-coupling theory for the pseudoscalar field with both direct and gradient coupling. The nucleon-nucleon interaction is treated phenomenologically and the "impulse" approximation employed. The behavior of the ratio $\frac{{\sigma }_{\mathrm{nonradiative}}}{{\sigma }_{\mathrm{radiative}}}$ for the $\mathrm{PS}$ theory is different from that for the $\mathrm{PV}$ theory. The charge-exchange scattering of a $\mathrm{PS}$ meson exhibits a minimum for forward scattering for both types of coupling but otherwise mirrors the behavior of the charge-exchange cross section for a neutron target. The elastic and inelastic scattering cross sections are comparable for an incident 25-Mev meson, and small energy transfers to the deuteron are favored, in contrast to the case in which the target nucleus is more complex.