80 Years of the liquid drop—50 years of the macroscopic–microscopic model

• We review the evolution of liquid-drop based nuclear mass models over 80 years.
• The original 1935 semi-empirical model of binding energies was accurate to 3 MeV.
• It was decisive for understanding radioactive decay and interpreting fission.
• The macroscopic–microscopic method [28] led to 0.6 MeV accuracy.
• The improvement is crucial for modeling nuclear stability and nucleosynthesis.

The liquid-drop model has its origins in the first mainstream model of the binding energy of nuclei, sometimes referred to as the semiempirical mass formula, which emerged in the mid 1930s. It is a beautiful example of a model that fulfills the criteria of what a theoretical model is and what an arbitrary parameterization of some data set is not: (1) it has a simple intuitive interpretation, (2) it was of enormous and immediate practical utility in interpreting nuclear experimental data such as radioactive decay and nuclear reactions, (3) it could predict binding energies of nuclei to which its parameters had not been adjusted, (4) it could be generalized to describe new, unanticipated phenomena such as fission, and (5) deviations of its predictions from experimental data yielded insight into nuclear structure and guided the development of more sophisticated models. Generalized liquid-drop models remain important because of the development of macroscopic–microscopic models which give important quantitative insight into ground-state structure and binding energies (nuclear masses) and many details of nuclear fission. We review these points and some associated historical milestones.

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