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基于AME2016发布的基态原子核质量数据, 分别从模型的精度及实验预言的中子新幻数两方面系统比较分析了八个普适核质量模型的可靠性及预言能力. 分区系统的计算了八个核质量模型预言的核质量均方根偏差, 分析发现对现有实验数据精确度较好的是Bhagwat和WS4两个模型. 通过分析中子壳能隙随中子数的变化趋势发现KTUY, WS3和WS4三个模型可以较好地再现中子新幻数N = 32引起的突变行为, 预言了在Cl和Ar同位素链中N = 32极有可能是新的幻数. 通过分析超重区域α衰变能随中子数的变化趋势发现FRDM12, WS3和WS4三个模型均可以较好地再现N = 152, 162的子壳现象, 且预言了对于质子数Z = 108—114同位素链在N = 184处原子核的寿命相对较长.The reliability and prediction ability of 8 global nuclear mass models is systematically analyzed in terms of the accuracy of the model and the new neutron magic number predicted by experiments based on the ground-state nuclear mass data from AME2016. The root-mean-square (RMS) deviations of nuclear mass predicted by 8 nuclear mass models are calculated by subregion, and find that the Bhagwat and WS4 models possess better accuracy to describe the existing experimental data. By analyzing the trend of the neutron shell energy gap varying with neutron number, it is found that the KTUY, WS3 and WS4 models can well represent the mutation behavior caused by the new magic number N = 32, and it is predicted that N = 32 is likely to be a new magic number in the Cl isotope chain and Ar isotope chain. By analyzing the variation trend of α decay energy in the superheavy region, it is found that the FRDM12, WS3 and WS4 models can reproduce the phenomena of subshell with N = 152 and N = 162 well, and predict the relatively long life of nuclei at the neutron number N = 184 for the isotope chain with proton number Z = 108—114. The comprehensive analysis shows that the mass model with good accuracy cannot reproduce shell evolution behavior. For example, the Bhagwat model has the same accuracy as the WS4 model, but it cannot reproduce the mutation behavior of the new magic number N = 32, 152 and 162. But the KTUY model and FRDM12 model can reproduce the new magic number behavior of N = 32, 152 and 162, respectively, although the RMS deviation is slightly larger. The RMS deviation of WS4 model is small and can describe the shell evolution behavior in the nuclear mass well.
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Keywords:
- nuclear mass model /
- root-mean-square deviation /
- new magic number
[1] Roubin A, Atanasov D, Blaum K, George S, Herfurth F, Kisler D, Kowalska M, Kreim S, Lunney D, Manea V, Minaya Ramirez E, Mougeot M, Neidherr D, Rosenbusch M, Schweikhard L, Welker A, Wienholtz F, Wolf R N, Zuber K 2017 Phys. Rev. C 96 014310
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图 1 八个核质量模型对轻核(8 ≤ Z < 28)、中等-I(28 ≤ Z < 50)、中等-II(50 ≤ Z < 82)、重核(82 ≤ Z < 100)以及超重(Z ≥ 100>)五个区域质量描述的均方根偏差
Fig. 1. Root-mean-square deviations of the mass of light (8 ≤ Z < 28), medium-I (28 ≤ Z < 50), medium-II (50 ≤ Z < 82), heavy (82 ≤ Z < 100), and super-heavy (Z ≥ 100) are calculated by the 8 nuclear mass models.
图 2 八个核质量模型的理论值与实验值的均方根偏差随ε的变化趋势
Fig. 2. Root-mean-square deviation between the predictions of the 8 nuclear mass models and the experimental values varies with the ε.
图 3 K, Ca, Sc, Ti和V同位素链的中子壳能隙随中子数的变化趋势
Fig. 3. Variation trend of neutron shell gaps in K, Ca, Sc, Ti and V isotope chains with neutron number.
图 4 八个核质量模型计算的K, Ca, Sc, Ti和V同位素链的中子壳能隙随中子数的变化趋势
Fig. 4. Neutron shell gaps of K, Ca, Sc, Ti and V isotopic chains calculated by 8 nuclear mass models vary with the neutron number
图 5 Cl和Ar同位素链中子壳能隙随中子数的变化趋势, 竖线表示误差
Fig. 5. Variation trend of neutron shell gaps of Cl and Ar isotope chains with neutron number, the vertical bar represents the error.
图 6 质子数
$ Z=100-110 $ 为偶数同位素链的α衰变能随中子数的变化趋势Fig. 6. Alpha decay energy of even isotope chains for the proton number
$ Z=100-110 $ vary with the neutron number.
图 7 八个核质量模型计算的质子数
$ Z=100-110 $ 为偶数同位素链的α衰变能随中子数的变化趋势Fig. 7. Alpha decay energy of even isotope chains for the proton number Z = 100-110 calculated by 8 nuclear mass models vary with the neutron number.
图 8 FRDM12和WS4模型计算的质子数
$Z=112- $ $ 124$ 为偶数同位素链的α衰变能随中子数的变化趋势, 竖线表示误差Fig. 8. Alpha decay energy of even isotope chains for the proton number Z = 100–110 calculated by the FRDM12 and WS4 models vary with the neutron number, the vertical bar represents the error.
表 1 八个核质量模型的基态质量、单中子分离能、单质子分离能、双中子分离能及双质子分离能的均方根偏差
Table 1. Root-mean-square deviations of the ground state mass, single-neutron separation energy, single-proton separation energy, two-neutron separation energy and two-proton separation energy of the 8 nuclear mass models.
模型 M/MeV Sn/MeV Sp/MeV S2n/MeV S2p/MeV KTUY 0.724 0.306 0.367 0.383 0.527 FRDM12 0.599 0.351 0.368 0.455 0.469 HFB27 0.517 0.424 0.446 0.423 0.464 DZ31 0.422 0.290 0.307 0.342 0.379 INM12 0.381 0.372 0.369 0.375 0.386 WS3 0.343 0.274 0.302 0.296 0.358 WS4 0.302 0.260 0.278 0.276 0.326 Bhagwat 0.301 0.282 0.296 0.306 0.329 
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[1] Roubin A, Atanasov D, Blaum K, George S, Herfurth F, Kisler D, Kowalska M, Kreim S, Lunney D, Manea V, Minaya Ramirez E, Mougeot M, Neidherr D, Rosenbusch M, Schweikhard L, Welker A, Wienholtz F, Wolf R N, Zuber K 2017 Phys. Rev. C 96 014310
Google Scholar
[2] Wang N, Liu M, Wu X Z 2010 Phys. Rev. C 81 044322
Google Scholar
[3] Wang Y Z, Gao Y H, Cui J P, Gu J Z 2020 Commun. Theor. Phys. 72 025303
Google Scholar
[4] Mo Q H, Liu M, Wang N 2014 Phys. Rev. C 90 024320
Google Scholar
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[6] Rosenbusch M, Ascher P, Atanasov D, Barbieri C, Beck D, Blaum K, Borgmann C, Breitenfeldt M, Cakirli R B, Cipollone A, George S, Herfurth F, Kowalska M, Kreim S, Lunney D, Manea V, Navrátil P, Neidherr D, Schweikhard L, Somà V, Stanja J, Wienholtz, F, Wolf R N, Zuber K 2015 Phys. Rev. Lett. 114 202501
Google Scholar
[7] Reiter M P, Ayet San Andrés S, Dunling E, Kootte B, Leistenschneider E, Andreoiu C, Babcock C, Barquest B R, Bollig J, Brunner T, Dillmann I, Finlay A, Gwinner G, Graham L, Holt J D, Hornung C, Jesch C, Klawitter R, Lan Y, Lascar D, McKay J E, Paul S F, Steinbrügge R, Thompson R, Tracy J L, Jr, Wieser M E, Will C, Dickel T, Plaß W R, Scheidenberger C, Kwiatkowski A A, Dilling J 2018 Phys. Rev. C 98 024310
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Google Scholar
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Google Scholar
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Google Scholar
[13] Ramirez E M, Ackermann D, Blaum K, Block M, Droese C, Düllmann C E, Dworschak M, Eibach M, Eliseev S, Haettner E, Herfurth F, Heßberger F P, Hofmann S, Ketelaer J, Marx G, Mazzocco M, Nesterenko D, Novikov Y N, Plaß W R, Rodríguez D, Scheidenberger C, Schweikhard L, Thirolf P G, Weber C 2012 Science 337 1207
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Google Scholar
[15] 周善贵 2014 物理 43 817
Google Scholar
Zhou S G 2014 Physics 43 817
Google Scholar
[16] 周善贵 2017 原子核物理评论 34 318
Google Scholar
Zhou S G 2017 Nucl. Phys. Rev. 34 318
Google Scholar
[17] Li P C, Zhang H F, Wang Y J 2017 Chin. Phys. C 41 114103
Google Scholar
[18] Düllmann C E, Block M 2018 Sci. Am. 318 46
Google Scholar
[19] Nazarewicz W 2018 Nat. Phys. 14 537
Google Scholar
[20] 李竹, 牛中明, 孙保华, 王宁, 孟杰 2012 物理学报 61 072601
Google Scholar
Li Z, Niu Z M, Sun B H, Wang N, Meng J 2012 Acta Phys. Sin. 61 072601
Google Scholar
[21] 何建军, 周小红, 张玉虎 2013 物理 42 484
He J J, Zhou X H, Zhang Y H 2013 Physics 42 484
[22] 李竹, 孙保华, 孟杰 2013 物理 42 505
Li Z, Sun B H, Meng J 2013 Physics 42 505
[23] Niu Z M, Niu Y F, Liang H Z, Long W H, Nikšic T, Vretenar D, Meng J 2013 Phys. Lett. B 723 172
Google Scholar
[24] Ma C, Li Z, Niu Z M, Liang H Z 2019 Phys. Rev. C 100 024330
Google Scholar
[25] Li Z, Miu Z M, Sun B H 2019 Sci. China, Ser. G 62 982011
Google Scholar
[26] 唐晓东, 李阔昂 2019 物理 48 633
Google Scholar
Tang X D, Li K A 2019 Physics 48 633
Google Scholar
[27] Möler P, Mumpower M R, Kawano T, Myers W D 2019 At. Data Nucl. Data Tables 125 1
Google Scholar
[28] 王猛, 张玉虎, 周小红 2020 中国科学: 物理学力学天文学 50 052006
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[31] Koura H, Tachibana T, Uno M, Yamada M 2005 Prog. Theor. Phys. 113 305
Google Scholar
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Google Scholar
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Google Scholar
[36] Goriely S, Chamel N, Pearson J M 2013 Phys. Rev. C 88 024308
Google Scholar
[37] Goriely S, Chamel N, Pearson J M 2013 Phys. Rev. C 88 061302(R
Google Scholar
[38] Goriely S, Chamel N, Pearson J M 2016 Phys. Rev. C 93 034337
Google Scholar
[39] Geng L S, Toki H, Meng J 2005 Prog. Theor. Phys. 113 785
Google Scholar
[40] Xia X W, Lim Y, Zhao P W, Liang H Z, Qu X Y, Chen Y, Liu H, Zhang L F, Zhang S Q, Kim Y, Meng J 2018 At. Data Nucl. Data Tables 121-122 1
Google Scholar
[41] Duflo J, Zuker A P 1995 Phys. Rev. C 52 R23(R
Google Scholar
[42] Zuker A P 2008 Rev. Mex. Fís. 54 129
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Google Scholar
[44] Sobiczewski A, Litvinov Y A 2014 Phys. Rev. C 89 024311
Google Scholar
[45] Sobiczewski A, Litvinov Y A 2014 Phys. Rev. C 90 017302
Google Scholar
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Google Scholar
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Google Scholar
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