Theoretical Study Of Fusion-fission Reactions At Energies Around The Coulomb Barrier

In recent decades,the synthesis mechanism of superheavy nuclei has been one of the hot fields of nuclear physics,and the fusion reaction of heavy ion is the only way to synthesize superheavy nuclei in the laboratory.The synthesis of superheavy nuclei by heavy-ion fusion reaction is generally considered to have three steps:capture process,fusion process,and survival process.In this thesis,we systematically study the evaporation residual(ER)cross sections of some systems based on the empirical coupled-channel model and the statistical model.The research content is divided into the following two parts:1.The ER cross sections of 48 reaction systems with quasifission barrier high enough are analyzed by using the empirical coupled-channel model and the statistical model.The experimental data of these reactions are systematically reproduced.We find that the value of af/an has a great influence on the calculated values of ER cross sections,which is caused by the fact that Γn/Γ in the statistical model is very sensitive to the value of af/an and will decrease with the increase of af/an.Therefore,the ratio of af(level density parameter in fission channel)to an(level density parameter in neutron-evaporation channel)plays a key role in reproducing the data appropriately.In addition,when the fissility parameter is 2/3<x<1,there is a good exponential relation between the ratio af/an and the fissility parameter.2.Based on the empirical coupled-channel model for calculating capture cross sections and the statistical model for describing survival probability,we propose an analytical formula for calculating the fusion probability for the reactions leading to superheavy nuclei.The cold-fusion and the hot-fusion reactions leading to superheavy nuclei have been systematically investigated.Using the same set of parameters,the data of the ER cross sections for both the cold-fusion and the hot-fusion reactions are systematically reproduced.Then,the ER cross sections for some reactions producing elements Z=119 and 120 are studied.It is found that the projectile-target combinations 50Ti+249Bk and 50Ti+249,251Cf are considered as the most promising reactions for the syntheses of the next two superheavy elements beyond Og.The maximal ER cross sections for 50Ti+249Bk are 48.2 fb at the incident energy Ec.m.=226 MeV.For 50Ti+249,251Cf,the maximal ER cross sections are about 10 fb at the incident energies around Ec.m.=232 MeV.