Synthesis of super-heavy elements: Role of uncertainty analysis in theoretical modeling

The existence of super-heavy elements (SHE) has been predicted by the nuclear shell model. However, the nuclear reaction theory for heavy systems has not been well established yet. Large discrepancies between quantitative predictions still persist because of the presence of the fusion hindrance phenomenon. The first aim of this PhD work is to investigate different models associated with the complete description of the fusion-evaporation reaction. Then, a complete uncertainty analysis, in combination with a newly-developed cascade code called KEWPIE2, is performed. By inspecting uncertainties due to parameters and models, it is clearly revealed that the fission barrier has the most crucial role to play in constraining the fusion models. How to determine the uncertainty associated with the fission barrier? Since we do not have enough reliable data, we propose to consider Bayesian inference by reversing the usual mode of thinking. Based upon the KEWPIE2 code with simulated pseudo-data, preliminary results tell us that the estimated uncertainty in the fission barrier appears to be quite sensitive to the number and precision of data points as well as the nuisance parameters. Furthermore, it is known that the fusion process and the fission barrier can be both described within the framework of the liquid-drop model. Thus, they should be correlated with each other. With the help of a simple liquid-drop mass formula and the regression theory, uncertainties in the model parameters as well as the correlation between the neutron-separation energy and fission barrier are inspected. The influence of their covariances on the survival probability is concretely investigated. (author)