Multiple constraints on nuclear mass formulas for reliable extrapolations

Abstract

Nuclear mass is responsible for many key processes in both nuclear physics and astrophysics. While the theoretical accuracy of masses has reached a quite astonishing level, the extrapolations among various predictions have been conflicting due to several possible reasons, such as the missing physics and overfitting problems in current formulas. Instead of the single target of binding energies, we make use of both the $\ensuremath{\alpha}$ decay energy and the Garvey-Kelson relations as multiple physical constraints on mass models to address the above issues to some extent. By means of the multiobjective optimization, the Bethe-Weizs\"acker--type and the Duflo-Zucker (DZ) mass models are carried out to perform such a study as specific examples. Thanks to very recent measured neutron-rich nuclei beyond the AME20, we further test the predictive power on two DZ-type formulas as accompanied by the impressive accuracy. The discrepancies between the predicted values of the DZ10 and the DZ33 can be significantly reduced, which implies the therapy of the overfitting phenomenon in some degree. This leads to lower uncertainties of extrapolations for the models themselves.