Off-Shell Effects in Pion-Deuteron Absorption

The cross section for the process ${\pi }^{+}+d\to p+p$ is calculated using a $\pi -N$ $t$ matrix obtained from a Lagrangian formalism. The $t$ matrix is provided with a suitable cutoff to damp the large (off-shell) momentum components and the total cross section is found to be strongly dependent on the cutoff range parameter taken, i.e., to how fast the $t$ matrix falls off as it is taken off shell. It is argued that this is to be expected physically and that this sensitivity might provide a means of studying the $\pi -N$ off-shell $t$ matrix.