How well do we understand the synthesis of heavy elements by heavy-ion induced fusion?

Experimental cross sections to synthesize heavy ion induced fusion reactions are confronted with calculations using the conventional picture of complete fusion after passing the barrier plus statistical deexcitation after complete equilibration. The sensitivity of the calculations to some of the parameters is demonstrated. Despite this sensitivity, a single parameter set is found that reproduces well the large body of data from experiments using actinide targets. By comparison, for the more symmetric entrance channels using targets around²⁰⁸Pb, we find a fusion hindrance that increases steeply with increasing compound nuclear charge. Predictions for a few reactions of future interest for the synthesis of heavy elements are also presented.