Empirical relations for the fusion cross sections of heavy ions

Simple relations for a calculation of the barrier height B, radius R and curvature ℏω 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 ${}^{12}$C + ${}^{12}$C with Z${}_1$Z${}_2$=36 to ${}^{58}$Ni + ${}^{124}$Sn with Z${}_1$Z${}_2$=1400. Substituting these formulas for B, R and ℏω 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.