Bayesian analysis on interactions of exotic nuclear systems

Abstract

Even though the Bayesian method has been proved to be powerful in the field of nuclear physics, it has not yet been implemented to study the properties of the reaction systems with exotic nuclei, for instance, the gross feature of the phenomenological interaction potential. So far, the optical model potential was typically evaluated by the traditional frequentist approach. However, contradictive conclusions were drawn, especially on the near-threshold behavior of the imaginary potential: threshold anomaly and abnormal threshold anomaly were derived for 6Li+209Bi and 6He+208Pb even with the same elastic scattering data. In this study, we first applied the Bayesian framework to analyze the elastic scattering data of 6Li+209Bi. It was found that the results of Bayesian statistics strongly depend on the imposed prior distributions. Therefore, the Bayesian method has to be used with extreme caution, since the improper prior knowledge could lead to completely wrong conclusions. Since the elastic scattering data is not informative enough to constrain the prior and posterior distributions, our analysis further indicates that the results from the non-constraint frequentist approach or the flat prior distribution with a reasonable physical-boundary can be employed as convincing prior knowledge of the Bayesian framework. Based on this result, we further applied the Bayesian approach to the transfer reaction 208Pb(7Li,6He)209Bi, to investigate the optical potentials of the neutron halo system 6He+209Bi in the outgoing channel. With the proper prior distributions, the Bayesian analysis on both the 6Li+209Bi and 6He+208Pb confirm the presence of the abnormal threshold anomaly. Therefore the applicability of the dispersion relation remains in doubt.