  This work presents an extensive exploration of scattering and tunneling
involving composite objects with intrinsic degrees of freedom. We aim at exact
solutions to such scattering problems. Along this path we demonstrate solution
to model Hamiltonians, and develop different techniques for addressing these
complex reaction-physics problems, discuss their applicability, and investigate
the relevant convergence issues. As examples, we study the scattering of a
two-constituent deuteron-like systems either with an infinite set of intrinsic
bound states or with a continuum of states that allows for breakup. We show
that the internal degrees of freedom of the projectile and its virtual
excitation in the course of reactions play an important role in shaping the
S-matrix and related observables, giving rise to enhanced or reduced tunneling
in various situations.
