Abstract
The constant-coupling and parabolic approximations to calculate the fusion cross section in coupled-channels problems are investigated in a simple two-channel problem. A comparison with the results of a full quantum mechanics calculation indicates that these frequently used approximations considerably overestimate the sub-barrier fusion cross sections. The discrepancy is traced back to the treatment of the transmission coefficient and we show that a very accurate cross section at all energies can be obtained with the use of WKB transmission coefficients.
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