Accuracy and Limitations of the Liquid Drop Model (LDM) in Nuclear Binding Energy Calculations

Abstract

This study aims to evaluate the accuracy of the Liquid Drop Model (LDM) in predicting atomic nuclear binding energy and binding energy per nucleon, by comparing it with reference values. LDM is based on the assumption that atomic nuclei can be treated as drops of incompressible fluid. Nuclear binding energy is calculated using the Semi-Empirical Mass Formula (SEMF), and the results are analyzed through linear regression comparison with empirical mass defect data. The calculation results show that the LDM produces small deviations for binding energy values in medium nuclei. However, this model is less accurate in predicting binding energy for light and heavy nuclei. The inaccuracy in heavy nuclei is explained by the dominance of prominent collective effects; here, the behavior of the nucleus is better explained by the interaction of all nucleons as a whole, rather than by the behavior of individual nucleons. This reinforces the basic principle of LDM in heavy nuclei. In addition, the calculation of binding energy per nucleon by LDM produces the highest binding energy peak in Krypton-80 with a value of 8.98 MeV/nucleon. This result differs from empirical reference values that place Iron-56 (Fe-56) as the most stable nucleus with the highest binding energy, namely 8.79 MeV/nucleon. This deviation in the stability peak highlights the limitations of LDM, particularly regarding the lack of consideration of quantum effects and nuclear shell structures that are more relevant to certain nuclei.