Accuracy in the determination of fusion barriers

Although there is no proof of the validity of the method, in a lot of papers, one computes the second derivative of the the experimental fusion cross section multiplied by the energy to extract the fusion barriers directly from the experiment. The purpose of this paper is to check the consistency of the method, as experimental points are sandwiched inside their error bars. We therefore analysed the validity, by giving ourselves a cross section σ(E), resulting from the coupled channel calculation code ECIS, upon which, in spite of the complexity of the calculations, we have full control. We took these calculated points as the ''experimental'' ones and we altered them by multiplication by small random numbers. This is intended to simulate the error bars, of which we want to examine the influence on the fusion barriers. We find that in spite of the rough predictions yielded by the second derivative method, this task requires data with a precision difficult to reach. Furthermore, a careful check of the predictions of this method for coupled channel calculations shows that, due to the errors bars, this approach adds spurious results. (orig.)