Assessment of approximations made in breakup-fusion descriptions

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Abstract
Three methods for calculating the breakup-fusion cross sections are compared; ours, and those of Baur and Trautmann and of Kasano and Ichimura. All three use the two-step and the spectator approximations. It will be shown first that, while ours does not make any further approximation, the other two make a few additional approximations. Errors caused by these additional approximations are assessed numerically. The errors are found rather large in general. A critical assessment of the formalism by Austern and Vincent, on which the work of Kasano and Ichimura was based, is also made.