  The quantum diffusion approach is extended to low energy fusion (capture)
reactions of light- and medium-mass nuclei. The dependence of the friction
parameter on bombarding energy is taken into account. A simple analytic
expression is obtained for the capture probability at extreme sub-barrier
energies. The calculated cross-sections are in a good agreement with the
experimental data. The fusion excitation functions calculated within the
quantum diffusion and WKB approaches are compared and presented in the
astrophysical $S$-factor representation.
