Synthesis of superheavy elements: Uncertainty analysis to improve the predictive power of reaction models

Abstract

Background: Synthesis of super-heavy elements is performed by heavy-ion fusion-evaporation reactions. However , fusion is known to be hindered with respect to what can be observed with lighter ions. Thus some delicate ambiguities remain on the fusion mechanism that eventually lead to severe discrepancies in the calculated formation probabilities coming from different fusion models. Purpose: In the present work, we propose a general framework based upon uncertainty analysis in the hope of constraining fusion models. Method: To quantify uncertainty associated with the formation probability, we propose to propagate uncertainties in data and parameters using the Monte-Carlo method in combination with a cascade code called KEWPIE2, with the aim of determining the associated uncertainty, namely the 95% confidence interval. We also investigate the impact of different models or options, which cannot be modeled by continuous probability distributions, on the final results. An illustrative example is presented in detail and then a systematic study is carried out for a selected set of cold-fusion reactions. Results: It has been rigorously shown that, at the 95% confidence level, the total uncertainty of the empirical formation probability appears comparable to the discrepancy between calculated values. Conclusions: The results obtained from the present study provide a direct evidence for predictive limitations of the existing fusion-evaporation models. It is thus necessary to find other ways to assess such models for the purpose of establishing a more reliable reaction theory, which is expected to guide future experiments on the production of super-heavy elements.