Fusion cross section at sub-Coulomb energies

The effective barrier at low energies is approximated by a Coulomb and parabolic barriers. A simple closed formula is obtained for the total reaction cross section which is the natural extension of Wong's results into the low energy domain. Theoretical predictions of averaged energy behaviour agree fairly well with various experimental results. The relation?ω ₀≧π(2kh ²Z₁Z₂ e ²/μ)^1/2 R ₀ ^?3/2 between the curvature and the extremum point of the nucleus-nucleus potential is suggested, based on low energy fusion experiments. By assuming equality sign, it is possible to extract the parameters of the barrier directly from experiment. Incidentally it is found that?ω ₀ remains persistently arround 4.5 MeV for all the reactions which have been investigated.