Bayesian Inference of Nuclear-Matter Density from Proton Scattering

Background: Proton elastic scattering at intermediate energy is widely employed as a tool for determining the matter radius of atomic nuclei. The sensitivity of the approach relies on high-resolution measurements at small scattering angles and low-momentum transfer. Under these conditions, the Glauber multiple scattering theory accurately describes the proton-nucleus elastic cross section. Purpose: Investigate the sensitivity of the Glauber multiple scattering theory to uncertainties associated with input parameters such as the nuclear-matter density distribution and nucleon-nucleon data. Method: A joint Bayesian inference was performed using 12 angular distributions of elastic scattering at different energies on ${}^{58}$Ni, ${}^{90}$Zr, and ${}^{208}$Pb targets. A Metropolis-Hastings algorithm was implemented to make an uncertainty quantification analysis for the input parameters used in the Glauber multiple scattering theory. Results: The experimental cross sections were fitted simultaneously using a joint Bayesian inference approach. Posterior probability density distributions of 42 input parameters were obtained from the analysis. A moderate correlation between the nuclear density parameters and the nucleon-nucleon cross sections was found. This correlation impacts the extraction of the nuclear-matter radius. Conclusions: The present analysis provided a consistent method for extracting the nuclear-matter density distribution of ${}^{58}$Ni, ${}^{90}$Zr, and ${}^{208}$Pb from data across different incident energies. Due to the correlation of the nucleon-nucleon cross sections with the other input parameters, a constrained Bayesian inference using free nucleon-nucleon cross section data was performed. The nuclear-matter radii obtained from the analysis are in good agreement with multiple results reported in the literature