This work presents an extensive exploration of scattering and tunnelinginvolving composite objects with intrinsic degrees of freedom. We aim at exactsolutions to such scattering problems. Along this path we demonstrate solutionto model Hamiltonians, and develop different techniques for addressing thesecomplex reaction-physics problems, discuss their applicability, and investigatethe relevant convergence issues. As examples, we study the scattering of atwo-constituent deuteron-like systems either with an infinite set of intrinsicbound states or with a continuum of states that allows for breakup. We showthat the internal degrees of freedom of the projectile and its virtualexcitation in the course of reactions play an important role in shaping theS-matrix and related observables, giving rise to enhanced or reduced tunnelingin various situations.
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