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

YUAN Cenxi

doi:10.11804/NuclPhysRev.34.01.110

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.

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

Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, Guangdong, China

Funds: National Natural Science Foundation of China(11305272); Specialized Research Fund for Doctoral Program of Higher Education(20130171120014); Guangdong Natural Science Foundation (2014A030313217); Pearl River S&T Nova Program of Guangzhou (201506010060)

Received Date: 2016-10-18

Publish Date: 2017-03-20

Key words:

Abstract: 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.

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Reference (14)

[1]	DOBACZEWSKI J, NAZAREWICZ W, REINHARD P G.J Phys G: Nucl Part Phys, 2014, 41: 074001.
[2]	MYERS W D, SWIATECKI W J. Nucl Phys, 1966, 81: 1.
[3]	MÖLLER P, NIX J R. At Data Nucl Data Tabl, 1995, 59:185.
[4]	POMORSKI K, DUDEK J. Phys Rev C, 2003, 67: 044316.
[5]	GORIELY S, CHAMEL N, PEARSON J M. Phys Rev Lett,2009, 102: 152503.
[6]	GORIELY S, CHAMEL N, PEARSON J M. Phys Rev C,2013, 88: 061302(R).
[7]	LIU M, WANG N, DENG Y, WU X. Phys Rev C, 2011, 84:014333.
[8]	WANG N, LIU M, WU X Z. MENG J. Phys Lett B, 2014734: 215.
[9]	ERLER J, BIRGE N, KORTELAINEN M, et al. Nature,2012, 486: 510.
[10]	YUAN C X. Phys Rev C, 2016, 93: 034310.
[11]	WANG M, AUDI G, WAPSTRA A H, et al. Chin Phys C,2012, 36(12): 1603.
[12]	YUAN C X, SUZIKI T, OTSUKA T, et al. Phys Rev C,2012, 85: 064324 (2012); YUAN C X, QI C, XU F R, et al.ibid, 2014, 89: 044327.
[13]	HEYDE K. Basic Ideas and Concepts in Nuclear Physics,2nd ed, 1999, IOP, Bristol.
[14]	STRUTINSKY V M. Nucl Phys A, 1967, 95: 420.

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

doi: 10.11804/NuclPhysRev.34.01.110

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