Markov Chain Monte Carlo Effective Range Analysis of Low-Energy Electron Elastic Scattering from Xenon

Modified effective range theory formulated as a Bayesian statistical model through the combination with Markov Chain Monte Carlo integration and fitting techniques is used to check the compatibility of different e(-)-Xe scattering data such as the total cross-sections, the momentum transfer cross-sections, and the differential cross-sections that were determined experimentally in the region of Ramsauer-Townsend minimum. On the basis of this predictive approach, the most probable value of the scattering length, (-6.51 +/- 0.05) a(0), is proposed. The present analysis suggests that the non-relativistic spinless effective range theory is suitable for the description of angular and energy dependencies of e(-)-Xe elastic scattering cross-sections below the threshold for first inelastic process.