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

A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly-bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of $B(E1)$ distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theoretical approaches that have been used to calculate reaction rates. 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.