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A relationship between the Coulomb inclusive break-up probability and theradiative capture reaction rate for weakly-bound three-body systems isestablished. This direct link provides a robust procedure to estimate thereaction rate for nuclei of astrophysical interest by measuring inclusivebreak-up processes at different energies and angles. This might be anadvantageous alternative to the determination of reaction rates from themeasurement of $B(E1)$ distributions through exclusive Coulomb break-upexperiments. In addition, it provides a reference to assess the validity ofdifferent theoretical approaches that have been used to calculate reactionrates. The procedure is applied to $^{11}$Li ($^{9}$Li+n+n) and $^6$He($^{4}$He+n+n) three-body systems for which some data exist.

Determining astrophysical three-body radiative capture reaction rates from inclusive Coulomb break-up measurements