Bootstrap method for constructing covariance matrices of optical-model parameters in the study of the threshold anomaly

Laboratorio TANDAR, Gerencia de Investigación y Aplicaciones, Comisión Nacional de Energía Atómica, B1650KNA San Martín, Buenos Aires, Argentina

^a e-mail: abriola@tandar.cnea.gov.ar

Published online: 13 September 2017

Abstract

The parameters of optical-model potentials are usually obtained by adjusting theoretical calculations to the corresponding experimental elastic-scattering data. It has been observed that the use of conventional covariance matrices for the evaluation of the uncertainties of the parameters obtained in this way, leads in general to unrealistically small values. This underestimate may be caused by either, an incorrect use of the statistical recipes, or by the lack of a systematic study of the robustness of the uncertainty values against the inclusion or exclusion of experimental data points within a given data set. In the present contribution we explore both factors. Regarding the first aspect we use a re-normalization for χ², similar to the one proposed by R.T. Birge. In the second case we use the Bootstrap method to create synthetic sets based on all the available experimental data in order to derive an effective covariance matrix. These procedures were applied to the re-analysis of elastic-scattering data for several heavy-ion systems at energies close to the Coulomb barrier