Empirical relations for the fusion cross sections of heavy ions

Abstract

Simple relations for a calculation of the barrier height B, radius R and curvature \( \hbar \omega\) parameters used in the Wong formula for an evaluation of the heavy-ion fusion cross section are presented. These relations are obtained by a fitting of 1995 experimental cross section values measured for 85 even-even heavy-ion systems ranging from 12C + 12C with \( Z_{1}Z_{2} = 36\) to 58Ni + 124Sn with \( Z_{1}Z_{2} = 1400\). Substituting these formulas for B, R and \( \hbar \omega\) into the Wong formula we can estimate both the fusion cross section of different spherical nuclei and the astrophysical S-factor. The value of the root-mean-square error of the decimal logarithm of the fusion cross section is 0.225.