Fusion cross section of light ions at sub-Coilomb energies

We investigate a barrier penetration model for the sub-Coulomb fusion of light ion systems and derive an analytic formula for the cross section. The validity of the model is checked against results based on a modified proximity potential which reproduces the fusion cross section at energies above the Coulomb barrier. The meaning of the parameters defining the model as well as the extrapolation of the formula at very low energies is discussed.