Methods of predicting `capture' cross sections,  i.e., cross sections for sticking of two colliding nuclei after overcoming the interaction barrier, are presented. Close links between the capture excitation functions and smearing of the interaction barrier are discussed. By using a new `polynomial fit' method of determining d² (E\sigma )/dE² values, the barrier distributions have been directly deduced for several precisely measured fusion excitation functions found in the literature, and compared with results of standard `point difference' method. Existing data on near-barrier fusion- and capture excitation functions for about 50 medium and heavy nucleus--nucleus systems have been analyzed using a simple formula obtained assuming Gaussian shape of the barrier distribution. Systematics of the barrier distribution parameters, the mean barrier and width of the distribution, are presented and proposed to be used together with the closed-form `error function formula' for predicting unknown capture cross sections in experiments on synthesis of super-heavy elements.

PACS numbers: 25.70.Jj