Background: The coupled-channel framework provides a good description for nuclear reactions, provided all relevant channels are included. However, practical applications are often performed in a reduced model space with only a single channel. To effectively account for the effects of missing channels, approximations developed for elastic scattering differ from those for fusion reactions.

Purpose: In this work, we investigate these different approximations used for fusion reactions and elastic scattering (or other direct reactions), by bringing them under the same coupled-channel framework.

Method: We perform coupled-channel calculations for reactions around the Coulomb barrier with a tightly bound projectile (${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$). We also perform continuum discretized coupled-channel calculations to study elastic (${}^8\mathrm{B}+{}^{58}\mathrm{Ni}$) and fusion (${}^6\mathrm{Li}+{}^{198}\mathrm{Pt}$) of loosely bound projectiles in the same energy regime.

Results: We contrast the coupled-channel results with those obtained in a single-channel approach with different assumptions for the effective interactions to shed light on the relevant absorption terms required for the two different reaction channels. Our results clearly show that, when the relevant channels are included in the coupled-channel framework, one can describe elastic and fusion cross sections using the same original Hamiltonian. However, our results also reveal a lack of consistency between the effective interaction required to successfully model direct processes and that used to describe fusion reactions when the problem is reduced to a smaller set of channels.

Conclusions: From our results, we can track the reason for this inconsistency: it stems from the contribution of nonelastic channels to fusion, a contribution that is lost when reducing the coupled-channel equations to a single equation in the elastic channel. In the cases discussed here, this lost information, while crucial in fusion processes, has no impact on elastic scattering.

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• Breakup reactions
• Direct reactions
• Elastic scattering reactions
• Low & intermediate energy heavy-ion reactions
• Nuclear forces
• Nuclear fusion
• Nuclear reactions
• Optical, coupled-channel & distorted wave models