A New Four-parameter Formula For Fusion Reaction Cross Section Above Barrier Energies

Heavy-ion nuclear reaction has always been one of the hot spots in nuclear physics experiment and theoretical research,In the calculations and analyses of nuclear reaction,the heavy-ion interaction potential U(r)between projectile nucleus and target nucleus is an extremely important physical quantity,which consists of nuclear potential VN(r),coulomb potential VC(r)and centrifugal potential Vcent(r).The Coulomb potential and the centrifugal potential can be accurately described,but the only uncertainty lies in the nuclear potential.Therefore,in order to understand the nuclear reaction process,it cannot be separated from the accurate description of the nuclear potential.Hence,we systematically introduce more than twenty kinds of models to describe the nuclear potential,among which we focus on several versions of the proximity potential.Fusion reaction is an important reaction mechanism in heavy-ion physics,and fusion barrier is of great significance to understand and analyze the mechanism of heavy ion fusion reaction.In general,the characteristic of fusion barrier is determined by the barrier height VB,its corresponding position RB,and the barrier curvature h?.By extracting the height and the position of the fusion barrier from the heavy-ion interaction potential and parameterizing the heavy-ion interaction potential with some known quantities,a pocket formula for calculating the structural parameters of the fusion barrier can be obtained.In this paper,the pocket formulas of four kinds of fusion barriers are systematically sorted out,and thirty-eight groups of reaction channels are selected.Four methods for determining the structural parameters of fusion barriers are used to carry out specific calculations,and the calculation accuracy of these methods is compared by error analysis.The results show that the calculation results of Zanganeh 2015 pocket formula agree best with the corresponding experimental data.In order to understand the mechanism of nuclear reaction,it is necessary to calculate the fusion cross section accurately.In order to facilitate the experimental design and observation of nuclear experts,it is necessary for theorists to provide a simple and accurate empirical formula for calculating the fusion cross section.In this paper,the Gupta-Kailas four-parameter formula for calculating the fusion cross section is introduced.However,since the four parameters in this formula are not fixed,it is not convenient to use this formula for experimental design and subsequent analysis.Now,forty years have passed since Gupta and Kailas came up with the formula,and many of the world's major nuclear physics laboratories have obtained new data in the past forty years.Based on Gupta-Kailas' four-parameter formula,we systematically collected and collated the fusion cross section data of the past decades,and refitted a new four-parameter formula(4PF)with more accurate parameters,which successfully reproduced the experimental data of the fusion cross section on the barrier.In addition,we use 4PF formula to calculate the fusion barrier parameters and analyze the error.By comparing the fusion barrier parameters obtained by other models,it can be seen that the fusion barrier parameters calculated by 4PF formula can reproduce the experimental data relatively well in general.