Heavy-ion fusion reactions of astrophysical interest

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be analyzed effectively using an uncomplicated straightforward elegant mathematical formula gleaned presuming diffused barrier with a Gaussian distribution. The mathematical formula for cross section of nuclear fusion reaction has been obtained by folding together a Gaussian function representing the fusion barrier height distribution and the expression for classical cross section of fusion assuming a fixed barrier. The variation of fusion cross section as a function of energy, thus obtained, describes well the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from ¹⁶O + ¹⁸O to ¹²C + ¹⁹⁸Pt, all of which were measured down to < 10 𝜇b. The agreement of the present theoretically calculated estimates with the measured values is excellent. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed. (author)