Discovery of new characterizations of parameter distributions in a semi- empirical mass model: an investigation by dividing an overdetermined system into numerous balanced subsystems* *Supported by the National Natural Science Foundation of China (11975209, U2032211, 12075287), the Physics Research and Development Program of Zhengzhou University (32410017), the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province (2017GGJS008)

Abstract

We propose and test a new method of estimating the model parameters of the phenomenological Bethe-Weizsäcker mass formula. Based on the Monte Carlo sampling of a large dataset, we obtain, for the first time, a Cauchy-type parameter distribution formed by the exact solutions of linear equation systems. Using the maximum likelihood estimation, the location and scale parameters are evaluated. The estimated results are compared with those obtained by solving overdetermined systems, e.g., the solutions of the traditional least-squares method. Parameter correlations and uncertainty propagation are briefly discussed. As expected, it is also found that improvements in theoretical modeling (e.g., considering microscopic corrections) decrease the parameter and propagation uncertainties.