Direct and sequential radiative three-body reaction rates at low temperatures

We investigate the low-temperature reaction rates for radiative capture processes of three particles. We compare direct and sequential capture mechanisms and rates using realistic phenomenological parametrizations of the corresponding photodissociation cross sections.Energy conservation prohibits sequential capture for energies smaller than that of the intermediate two-body structure. A finite width or a finite temperature allows this capture mechanism. We study generic effects of positions and widths of two- and three-body resonances for very low temperatures. We focus on nuclear reactions relevant for astrophysics, and we illustrate with realistic estimates for the $\alpha$-$\alpha$-$\alpha$ and $\alpha$-$\alpha$-$n$ radiative capture processes. The direct capture mechanism leads to reaction rates which for temperatures smaller than 0.1 GK can be several orders of magnitude larger than those of the NACRE compilation.