Statistical error analysis for phenomenological nucleon-nucleon potentials

Abstract

Nucleon-nucleon potentials are common in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard least-squares ${\ensuremath{\chi}}^{2}$ fitting procedure and apply, along with more conventional tests, a tail-sensitive quantile-quantile test as a simple and confident tool to verify the normality of residuals. We show that the fulfillment of normality tests is linked to a judicious and consistent selection of a nucleon-nucleon database. These considerations prove crucial to a proper statistical error analysis and uncertainty propagation. We illustrate these issues by analyzing about 8000 proton-proton and neutron-proton scattering published data. This enables the construction of potentials meeting all statistical requirements necessary for statistical uncertainty estimates in nuclear structure calculations.