Which Nuclei are Well Described by Liquid Drop Model: A Statistical Study Based on Uncertainty Decomposition Method

Which data are well described by a theoretical model? Such questions can be answered through the physical origin of the model. For example, the liquid drop model (LDM) well describes the heavy and far from shell nuclei. Because the liquid-drop assumption is more suitable for nuclei with more nucleons and LDM does not include the shell effect. Such answer is qualitative and needs a clear view on the physical origin of the model. Is it possible to give an semi-quantitatively answer only from the mathematical form of the model and the observed data. In the present work, the recently suggested uncertainty decomposition method (UDM) is used to answer which nuclei are well described by LDM. The residues between LDM and the observed data can be decomposed through UDM to systematic and statistical uncertainties, which represent the uncertainty of the deficiency of the model and the indeterminate parameters, respectively. Based on UDM, the chart of nuclides are semi-quantitatively divided into three parts, areas dominated by the systematic and statistical uncertainties, and the cross area. Contrary to the common sense, the well described nuclei by LDM are not the nuclei with small residues, but actually the nuclei of which the residues are dominated by the statistical uncertainty. These nuclei are indeed the heavy and far from shell nuclei, which agrees with the physical consideration of LDM. But only the mathematical form of the model and the experimental data are needed during the use of UDM. The nuclides dominated by the statistical uncertainty can be well described by LDM (standard deviation less than 0.7 MeV) with parameters fitting to these nuclei.