Analysis of nuclear structure effects in sub-barrier fusion dynamics using energy dependent Woods-Saxon potential

Abstract

The fusion dynamics of various projectiles (${}^{16}_{8}$O, ${}^{27}_{13}$Al and ${}^{37}_{17}$Cl) with the ${}^{70,72}_{32}$Ge-isotopes is analyzed using the energy dependent Woods-Saxon potential model (EDWSP model) and the coupled channel formulation. The impacts of the inelastic surface excitations of fusing nuclei have been examined using the coupled channel model and by inclusion of appropriate number of the intrinsic channels, the observed fusion enhancements can be reasonably explained for all fusing systems. The magnitude of the sub-barrier fusion enhancement is found to be increasing with the increase of deformation parameter associated with the colliding systems. Furthermore, the optimum choice of the static Woods-Saxon potential and the EDWSP model are simultaneously tested along with the Wong's approximation for explanation of the fusion of ${}^{16}_{8}$O + ${}^{70,72}_{32}$Ge, ${}^{27}_{13}$Al + ${}^{70,72}_{32}$Ge and ${}^{37}_{17}$Cl + ${}^{70,72}_{32}$Ge reactions. The theoretical predictions obtained by using the static Woods-Saxon potential model are found to be substantially smaller than the experimental data particularly at below barrier energies. In contrast, the EDWSP model based calculations provide an adequate description of the observed fusion enhancement of the chosen reactions. This unambiguously reveals that the discrepancies between theoretical results obtained through the single barrier penetration model and the experimental data can be partially or fully removed if either one makes the use of the EDWSP model along with the Wong's approximation or includes the intrinsic channels associated with the fusing systems in coupled channel calculations. In addition, the EDWSP model based predictions are capable of recovering an agreement with the fusion data within 10%. For chosen reactions, only at 7 fusion data points out of 77 fusion data points does the deviation exceed 5% while 70 fusion data points lie within 5%. Therefore, the EDWSP model based calculations are able to provide close agreement with the fusion data points at above barrier energies within 5% with a probability more than 90%.