A Bayesian R-matrix analysis of low-energy dt fusion

The dt fusion reaction ${}^2$H + ${}^3$H $\rightarrow$ ${}^4$He + n is important for nuclear fusion applications. It is also part of the BBN chain. There are several precise measurements of this cross section in the energy range 5-250 keV. These data sets are, however, not consistent with one another. We report on the use of Bayesian methods to analyze this data set, in the spirit of Ref. [1] . Employing the quoted point-to-point and common-mode errors from the original publications and a single-level R-matrix parameterization we find $S(40~{\rm keV})=26.57 \pm 0.06$ MeV $\cdot$ b, but with a poor $\chi^2$ per degree of freedom. We find that the point-to-point errors on some data sets must be inflated to obtain a statistically consistent data base. Different possibilities for the inflation yield consistent results for $S(40~{\rm keV})$, as does a three-level R-matrix parameterization. Our preliminary result is $S(40~{\rm keV})=25.48 \pm 0.17$ MeV $\cdot$ b, which is a lower central value and bigger error bar than Ref. [1]. The use of parallel tempering, and the elimination of redundant variables in the R-matrix parameterization allowed us to fully sample the posterior parameter probability density. \newline [1] R. S. de Souza {\it et al.}, Phys. Rev. C {\bf 99}, 014619 (2019)