Improved determination of the fusion barrier distribution

The usual formula employed to estimate the barrier distribution in fusion reactions contains a systematic error. The origin of this error is related to the numerical approximation of the second derivative appearing in the expression of the barrier distribution. We show how to approximately correct for this systematic error. Previous determinations of the uncertainties in the barrier distribution, that did not include this error, could be severely underestimated. Furthermore, we find that minimization of the total error leads to an optimal energy grid at which the fusion cross section data should be taken