  We investigate the triple-alpha reaction at low energies, by assuming a
direct process. The Coulomb potential of three $\alpha$ particles is examined
carefully. The three-body continuum wave functions are generated by calculating
an adiabatic potential barrier. We discuss the influence of the $\alpha\alpha$
potential, and compare our reaction rates with the literature. The reaction
rate at $T=0.01$\,GK is about 10$^3$ times larger than that of NACRE.
