Uncertainties of optical-model parameters for the study of the threshold anomaly

TL;DR

This paper investigates the uncertainties in optical-model parameters used in analyzing elastic-scattering data near the Coulomb barrier, emphasizing the importance of robust uncertainty evaluation for interpreting the threshold anomaly.

Contribution

It introduces a consistent approach using statistical and bootstrapping methods to evaluate parameter uncertainties, re-analyzing key nuclear scattering data.

Findings

Uncertainties significantly affect the interpretation of the threshold anomaly.

Previous studies lacked a standardized criterion for uncertainty evaluation.

Bootstrapping provides a robust alternative for uncertainty estimation.

Abstract

In the analysis of elastic-scattering experimental data, optical-model parameters (usually, depths of real and imaginary potentials) are fitted and conclusions are drawn analyzing their variations at bombardment energies close to the Coulomb barrier (threshold anomaly). The judgement about the shape of this variation (related to the physical processes producing this anomaly) depends on these fitted values but the robustness of the conclusions strongly depends on the uncertainties with which these parameters are derived. We will show that previous published studies have not used a common criterium for the evaluation of the parameter uncertainties. In this work, a study of these uncertainties is presented, using conventional statistic tools as well as bootstrapping techniques. As case studies, these procedures are applied to re-analyze detailed elastic-scattering data for the $^{12}$C + $^{208}$Pb and the $^6$Li + $^{80}$Se systems.