Conventional nuclear mass formulas, predicated on the charge independence of nucleon-nucleon ($NN$) interactions, generally parametrize the neutron-proton asymmetry $[I=(N-Z)/A]$ using even powers or absolute values. Previously, an $I^3$ term was incorporated into the classical liquid drop model to examine the influence of isospin symmetry breaking (ISB) on nuclear mass. Although this term captures the ISB effect especially in the mass region of large isospin asymmetry, its directly fitted coefficient is often overshadowed by the dominant macroscopic background. This may lead to numerically entangled and physically unreasonable values, which would undermine the credibility of subsequent conclusions regarding the breaking effect. To address this issue, this paper utilizes a double-difference analysis of binding energies to extract a more physically rational coefficient for the $I^3$ term. Benefiting from the isospin-related terms, the coefficients of these terms all have been refined, during which the volume symmetry energy coefficient was readjusted to around −29 MeV. This is slightly lower than the typical results found in previous models. Furthermore, the ratio of surface symmetry energy coefficient to the volume symmetry energy coefficient is in the range of 1.6–1.8, which is in good agreement with the results reported in previous works. More importantly, the value of the ISB term coefficient, as expected, was refined to $-3.7\pm 0.65$ MeV. Although the contribution of this term to nuclear mass in the liquid drop model is small, the extracted values remain highly stable, particularly when approaching the neutron-rich region.

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• Binding energy & masses
• Nuclear forces
• Nuclear structure & decays
• Symmetry energy
• Collective models