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