  In this work we evaluate the imaginary part of the isobar $\Delta$
self-energy $\Sigma_{\Delta}$ from the two-body absorption process
$\Delta+N\rightarrow 2N$. This contribution is calculated using a recently
developed non-relativistic scheme, which allows for an evaluation of the
self-energy with a basis of single-particle states appropriate for both bound
hole states and for particle states in the continuum. In order to test the
medium dependence of the self-energy, we calculate the two-body absorption term
$\Sigma_{\Delta}^{A2}$ for several finite nuclei with $N=Z$, i.e.\ $^{16}$O,
$^{40}$Ca and $^{100}$Sn. The resulting self-energy, which is energy dependent
and non-local, is compared with a simple parameterization derived from nuclear
matter.
