A Comparative Study Of Double Folding Potential And Other Nuclear-Nuclear Potentials

The heavy ion nucleus-nucleus interaction potential is one of the key physical quantities to deeply understand the fusion reaction mechanism,which can be generally expressed as the sum of the nuclear potential,Coulomb potential and centrifugal potential of the reaction system.In the actual calculation,the centrifugal potential is generally not considered,and this part of the interaction has been included in the specific calculation codes.Therefore,the key of the calculation for nucleus-nucleus potential is how to accurately calculate the nuclear potential and the Coulomb potential.Different from the common phenomenological models,which the nuclear density distribution and the charge density distribution are relatively simple,and the double-folding model（DFM）strictly deal with the influence of beforementioned two kinds of density distributions on the extraction of nucleus-nucleus interaction potential in nuclear finite-range.For the purpose of systematic research,seven groups of spherical projectile-target nuclear reaction systems and six groups of deformed target nuclear reaction systems,respectively,are selected for numerical calculation.Then,combined with the potential parameters obtained by DFM fitting,the fusion excitation functions（FEFs）of the above two kinds of heavy-ion reaction systems were calculated by the coupled channel model,and compared with the results with the modified Woods-Saxon（MWS）potential parameters.The results of spherical projectile-target systems show that the nuclear potential calculated by DFM is lower than that calculated by other phenomenological models,and the downward trend of nuclear potential calculated by DFM is more obvious at a critical position of the distance between two nuclei,which is related to the Coulomb parameter and mass asymmetry parameter of the reaction system.The stronger the symmetry of the reaction system,the more backward for the critical position.At the critical position,the difference between the Coulomb potentials calculated by DFM and the phenomenological model increases with the increase of the Coulomb parameters of the reaction system,which further indicates that the calculation of the Coulomb potential in DFM will determine the accuracy and reliability of the models to describe the heavy-ion nucleus-nucleus potential.The results of the FEF show that the nucleus-nucleus potential parameters extracted by DFM perfectly reproduce the FEFs of the lighter reaction system.However,with the increase of the mass asymmetry of the reaction system,although the potential parameters fitted by DFM can still perfectly reproduce the FEF in the above-barrier regions,the experimental data in the sub-barrier regions are underestimated.This is because as the distance between the two nuclei decreases,the reaction mechanism involved is more complex;for the heavy systems,the compound nuclei will be deexcited through nuclear fission and the evaporation of light particles.As the mass asymmetry coefficient of system decreases,the calculations of the potential parameters fitted by DFM underestimates the FEF in the sub-barrier energy region.This is not only related to the increase of the reaction channel and the complexity of the reaction mechanism,but also related to the coupling channel effect for the projectiles and the targets in the low-lying states.The results for the deformed targets show that similar to the spherical targets,the nuclear potential calculated by DFM is lower than those of other phenomenological models.With the decrease of the distance between the two nuclei,the decrease of the nuclear potential calculated by DFM is much larger than that of other phenomenological models.The above phenomenon is most obvious when the azimuth angle between the two nuclei is 150°.In addition,for the deformed target systems,there is still a critical position where the nuclear potential changes.When the azimuth angle of the two nuclei is 90°,the critical position parameter is toward front end,because the two-core line is perpendicular to the symmetry axis of the target.The results of the fusion excitation curve show that the calculation of the FEF of the potential parameters fitted by DFM overestimates the FEF of ¹⁶O+¹⁴⁸Sm system.In contrast,the MWS potential underestimates the curve of the system,and the law generally exists in several reactions of ³²S+⁹⁶Zr,¹⁶O+¹⁵⁴Sm and ¹⁶O+²³²Th.The main reason is that for the beforementioned reaction channels,the experimental data is the evaporation residue cross section,and the calculations includes the contribution of other reaction channels in addition to the evaporation residue cross section.For the ⁴⁰Ca+⁹⁶Zr reaction channel,the potential parameters fitted by DFM overestimate the FEFs in the above-barrier regions and underestimate the excitation functions in the sub-barrier region,which is due to the obvious coupled channel effect in the sub-barrier region.