Calculation of complete fusion cross sections of heavy ion reactions using the Monte Carlo method

The nucleus-nucleus potential for the fusion reactions ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, and ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ has been calculated using the Monte Carlo method. The results obtained indicate that the technique employed for the calculation of the nucleus-nucleus potential is an efficient one. The effects of the spin and the isospin terms have also been studied using the same technique. The analysis of the results obtained for the ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ reaction reveal that the isospin-dependent term in the nucleon-nucleon potential causes the nuclear potential to drop by an amount of 0.5 MeV. The analytical calculations of the fusion cross section, particularly those at energies less than the fusion barrier, are in good agreement with the experimental data. In these calculations the effective nucleon-nucleon potential chosen is of the M3Y-Paris potential form and no adjustable parameter has been used.

Figure 1

The effect of the spin and the isospin terms of the M3Y potential on the potential of the ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}=51.55$ MeV.

Figure 2

Comparison between the analytically calculated fusion cross sections using the potential obtained by the Monte Carlo method and the experimental data for the fusion reaction ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$. The solid and dash lines show the excluding and including effect of the spin and the isospin on the cross-section calculations. The experimental data of the fusion cross sections are taken from Ref. [14].