Uncertainty analysis of the nuclear liquid drop model

This study made a statistical analysis on the correlation and uncertainty of parameters in the classical liquid drop mass formula (namely BW3 type) via the regression way, along with the theoretical impact of error propagation. Within the improved BW3 formula, the total deviation between evaluation and experiment can be reduced to MeV, involving the reduction from 2.89 (2.42) MeV to 1.92 (1.89) MeV in the proton(neutron)-dripline region. Through trend coefficients and Pearson linear-correlation analysis, obvious collinearity was identified between volume, surface, Coulomb and curvature terms, with notable correlation among high-order symmetry energy and surface symmetry terms. Considering the impact of multicollinearity on model accuracy, the ridge regression validation confirmed that the standard deviation of the present mass formula has reached the optimal point without additional physical terms. The theoretical derivation of the distribution in the binding energy error was then achieved through error propagation analysis. Across the nuclide chart, the error uncertainty of mass predictions varies from 1.996 keV to 124.469 keV, demonstrating a convex trend of the initial decrease of evaluation error following by the increasing versus the neutron number.