Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: an investigation into propagating uncertainties for independent model parameters

Abstract

Based on the Monte Carlo approach and conventional error analysis theory, taking the heaviest doubly magic nucleus $$^{208}\hbox {Pb}$$ as an example, we first evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energy in the phenomenological Woods–Saxon mean field. Accepting the Woods–Saxon modeling with uncorrelated model parameters, we found that the standard deviations of single-particle energy obtained through the Monte Carlo simulation and the error propagation rules are in good agreement. It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties. Further, the correlation properties of the single-particle levels within the domain of input parameter uncertainties are statistically analyzed, for example, with the aid of Pearson’s correlation coefficients. It was found that a positive, negative, or unrelated relationship may appear between two selected single-particle levels, which will be extremely helpful for evaluating the theoretical uncertainty related to the single-particle levels (e.g., K isomer) in nuclear structural calculations.