Calculation of the coefficients of the Bethe-Weizsäcker Semi-Empirical Formula

Abstract

In our work, a numerical method optimizing the five energy coefficients of the semi empirical mass formula is presented. This method is based on the least-squares adjustments method on the atomic masses of 2550 different nuclides from the last update of the atomic mass evaluation, AME2020 published in February 2021. This lead to the resolution of a linear system which is solved by iterations according to the Gauss-Seidel method. The obtained set of formula coefficients allowed us to reproduce most of the experimental values with a very good agreement for A>50, yielding relative errors that oscillate between less than 0.05% and 1.5%.