  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.
