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We study the fine-structure constant dependence of the rates of some selected radiative capture reactions within the framework of so-called Halo Effective Field Theory in order to assess the adequacy of some assumptions made on the Coulomb penetrability. We find that this dependence deviates from that implied by a parameterization of the cross sections of this effect via a simple penetration factor. Some features of this fine-structure dependence are discussed, in particular its potential impact on the abundances of the light elements in primordial nucleosynthesis.

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