Direct and sequential four-body recombination rates at low temperatures

We investigate four-body nuclear reactions in stellar environments contributing to the creation of light nuclei, exemplified by $^{9}\mathrm{Be}$ and $^{12}\mathrm{C}$. The originally assumed process is radiative capture, where clusters combine into excited final nucleus photon emission populates stable ground states. Instead, we consider recombination a spectator particle replaces photon. first develop elaborate formalism for both direct sequential capture processes, decaying three-body resonance formed without with population an intermediate two-body resonance, respectively. To facilitate calculations practical applications parametrize involved cross sections as done successfully previous computations reaction rates. lowest-lying states their dominant contributions at low temperatures. calculate compare production rates different processes. mechanism dominates many orders magnitude temperature, stepping stones are energetically too expensive use. At somewhat higher temperatures these two mechanisms become comparable. Comparison reveals already formally, but also numerically, that must dominate sufficiently high densities. Numerical values given all function temperature density. relative importance exhibited.