Improvement of nuclear semi-empirical mass formula by including shell effect*

Abstract Shell effect plays an important role in nuclear mass predictions, especially for the nuclei around the magic numbers. In this study, a new semi-empirical shell correction term is constructed to improve the mass description of the Bethe-Weizsäcker (BW) formula. For nuclei with , the root mean square (rms) deviation of the newly proposed formula with respect to the latest nuclear mass evaluation dataset AME2020 is 0.887 MeV, inducing a 72.23% reduction compared to the rms deviation of 3.194 MeV for the BW formula. The deviations between the theoretical predictions and experimental data are within 1.5 MeV for 91.90% of the nuclei. In addition, the new mass formula significantly improves the predictions of the binding energies for magic nuclei. The rms deviation of our formula for the binding energy of magic nuclei is only 1.065 MeV, which is a 80.80 reduction compared with that of the BW formula.