Theoretical predictions of nuclear binding energy for the observed nuclei: the influence of coefficients and terms in a semi-empirical mass formula

Abstract

The aim of this study is to calculate the nuclear binding energy for the 2457 nuclei which experimentally observed, as tabulated in the atomic mass evaluation AME2020, by using the semi-empirical mass formula based on the renowned liquid drop model (LDM). The Bethe-Weizsäcker (BW) mass formula-four terms (BWMF-4T) is extended to incorporate an additional six terms, resulting in a formula of ten terms. Our findings demonstrate commendable accuracy and reliability, as substantiated by the acceptable level of uncertainty observed when compared them to experimental data and existing models. The influence of coefficients and terms in the semi-empirical mass formula has been determined. All possible combinations of the terms are fitted in turn to the measured nuclear masses, and the outcomes are analyzed in order to reveal correlations and mutual influences between the various terms in all observed mass regions of the periodic table. The fitted surface energy and symmetry coefficients in the Semi-empirical mass formula-ten terms (SEMF-10T) are remaining 26.4 and 33.3 MeV respectively. In contrast, coefficients fitted in the classic BW formula with and without one or two additional terms are around 17 and 23 MeV, respectively. The interplay between different terms in this mass formula is found to be significant and interesting.