Barrier penetration effects in the triple-alpha reaction at low energies

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.