Measurment Of ¹²C+¹³C Fusion Cross Section Around Coulomb Barrier Energies

Carbon burning driven by the ¹²C+¹²C fusion is a crucial process for nucleosynthesis.Unfortunately,because of the very low cross section,direct measurements at energies in Ec.m.=1-3 MeV are very difficult.And the carbon isotope fusion reactions has systematically studied at the University of Notre Dame?UND?.The ¹²C+¹³C system can provide an upper limit for ¹²C+¹²C and a test of the predictive powers of various theoretical models for the carbon fusion cross sections at deep sub-barrier energies.Due to low reaction cross section and the large background,it is very difficult to direct measure the ¹²C+¹³C cross section through the method of in-beam ?-ray spectroscopy under deep sub-barrier energies.Therefore offline activation measurement has became an effective method.There are two parts in this thesis.first is the in-beam irradiation,the ¹³C beam was produced by a cesium sputter ion source and injected into a HVEE Tandem 6 MV electrostatic accelerator of Peking University,and impinged a thin carbon target,varying the beam energies between 9.2 and 12.2 MeV in steps of 0.2 MeV.And the second part is off-line ?-ray measurement,we used coincidence method to measure the ? decay radiation from 24Na?T1/2=15 h?,the residual of proton evaporation channel.Finally,we gained the cross section of ¹²C(¹³C,p)24Na reaction,and used the theoretical branching ratio given by Hauser-Feshbach model to deduce the total fusion cross section of ¹²C+¹³C.Then we compared with the data from Dayras?1976?and Dasmahapatra?1981?,such both used in-beam ?-ray spectroscopy method.These three different methods have been exploited to perform the fusion cross section measurements for ¹²C+¹³C.Although the statistical model calculations in all these three methods have to be used to convert the ?-ray yields into the total fusion cross sections,the systematic uncertainty induced by the statistical corrections has not been studied very well.After we compared the difference for the three different types of detection methods and the preliminary results,included two non-statistical data from Carnelli and Kovar,the systematic uncertainty of statistical model has been determined to 14%.