  In a previous paper, it was shown that a soluble model can be constructed for
the description of a decaying system in analogy to the Lee-Friedrichs model of
complex quantum theory. It is shown here that this model also provides a
soluble scattering theory, and therefore constitutes a model for a decay
scattering system. Generalized second resolvent equations are obtained for
quaternionic scattering theory. It is shown explicitly for this model, in
accordance with a general theorem of Adler, that the scattering matrix is
complex subalgebra valued. It is also shown that the method of Adler, using an
effective optical potential in the complex sector to describe the effect of the
quaternionic interactions, is equivalent to the general method of Green's
functions described here.
