Prediction of ground-state spin in odd-<i>A</i> nuclei within decision tree

Wen Hu-Feng; Shang Tian-Shuai; Li Jian; Niu Zhong-Ming; Yang Dong; Xue Yong-He; Li Xiang; Huang Xiao-Long

doi:10.7498/aps.72.20230530

Abstract

Ground-state spin, as a fundamental parameter of nucleus, has consistently been a hot topic in research on nuclear data and structure. In this paper, we extensively investigate the odd-mass nuclei (odd-A nuclei) on the nuclide chart by using decision trees, including odd-proton nuclei (odd-Z nuclei) and odd-neutron nuclei (odd-N nuclei), and train ground-state spin prediction models of odd-Z nuclei and odd-N nuclei. In the case of randomly dividing the training set and validation set in a ratio of 75% to 25%, the accuracy rate of the training set and validation set for odd-Z nuclei reach 98.9% and 79.3%, respectively. The accuracy rate of the training set and validation set for the odd-N nuclei reach 98.6% and 71.6%, respectively. At the same time, by 1000 random selections of training set and validation set, after being validated repetitively, the standard error of the accuracy rate obtained can be less than 5%, further verifying the reliability and generalization performance of the decision tree. On the other hand, the accuracy rate of decision tree is much higher than those of theoretical models commonly used in nuclear structure research, such as Skyrme-Hartree-Fock-Bogoliubov, covariant density functional theory, and finite range droplet model. Next, by taking all spin-determined odd-Z nuclei and odd-N nuclei as a learning set, the ground-state spin values for 254 spin undetermined but recommended odd-Z nuclei and 268 spin undetermined but recommended odd-N nuclei are predicted, with the predicted set coincidence rates reaching 68.5% and 69.0%, respectively. Finally, four odd-mass number chains, i.e. Z = 59, Z =77, N = 41, and N = 59, are selected to compare the learning (prediction) results of the decision tree with the experimental (recommended) values of the corresponding nuclei, and to discuss the differences and similarities in the results given by the three theoretical models, thereby further demonstrating the research and application value of the decision tree in the ground-state spin of nuclei.

Keywords:

Authors and contacts

1.
School of Physics, Jilin University, Changchun 130012, China
2.
School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
3.
Key Laboratory of Nuclear Data, Chinese Academy of Atomic Energy Sciences, Beijing 102413, China

Corresponding author: Li Jian, jianli@jlu.edu.cn ; Yang Dong, dyang@jlu.edu.cn ;

Funds: Project supported by the Natural Science Foundation of Jilin Province, China (Grant No. 20220101017JC), the National Natural Science Foundation of China (Grant Nos. 11675063, 11875070, 11935001), the Key Laboratory of Nuclear Data Foundation, China (Grant No. JCKY2020201C157), and the Anhui Project, China (Grant No. Z010118169)

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References

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[73]	Akkoyun S, Bayram T 2014 Int. J. Mod. Phys. E 23 1450064 Google Scholar
[74]	Wang X, Zhu L, Su J 2021 Phys. Rev. C 104 034317 Google Scholar
[75]	Wu D, Bai C, Sagawa H, Nishimura S, Zhang H 2021 Phys. Rev. C 104 054303 Google Scholar
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Cited By

图 1 奇A核基态自旋实验值分布, 用不同颜色表示不同自旋值　(a)奇Z核; (b)奇N核

Figure 1. Experimental ground-state spin of odd-A nuclei: (a) Odd-Z nuclei; (b) odd-N nuclei. Different values are represented by different colors.

DownLoad: Full-Size Img PowerPoint

图 2 训练集和验证集的正确率随最大树深的变化　(a)奇Z核; (b)奇N核

Figure 2. Change of accuracy of training set and validation set with the maximum depth of decision tree: (a) Odd-Z nuclei; (b) odd-N nuclei

DownLoad: Full-Size Img PowerPoint

图 3 学习集正确率随最大树深的变化

Figure 3. Change of accuracy of learning set with the maximum depth of decision tree

DownLoad: Full-Size Img PowerPoint

图 4 基于最大树深为11的决策树模型得到的原子核基态自旋学习集和预测集的结果, 其中与实验值相同(不同)的用红色实心(空心)圆圈表示; 与推荐值相同(不同)的用蓝色实心(空心)方块表示; 没有推荐值的用蓝色实心三角表示　(a)奇Z核; (b)奇N核

Figure 4. Learning set and prediction set of the ground-state spin based on the decision tree model with the maximum depth of 11: (a) Odd-Z nuclei; (b) odd-N nuclei. The one same (different) as the experimental value is represented by a red solid (hollow) circle; the one same (different) as the recommended value is represented by blue solid (hollow) square; those with no recommended value are represented by blue solid triangles.

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图 5 基于决策树得到的质子数$ Z=59 $、$Z=77$的同位素链, 以及中子数$ N=41 $、$ N=59 $的同中异位素链原子核的基态自旋值, 并与SHFB、CDFT、FRDM预测结果和相应实验值、推荐值结果的比较

Figure 5. The ground-state spin of $ Z=59 $ and $Z=77$ isotopic chains (left) and $ N=41 $ and $ N=59 $ isotonic chains (right) are obtained based on the decision tree, and compared with the predicted results of SHFB, CDFT, FRDM and the corresponding experimental and recommended values.

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表 1 最大树深为11时取1000次随机重复验证, 分别得到奇Z核和奇N核的训练集与验证集正确率平均值和正确率标准误差

Table 1. Average and standard error of the accuracy of the training set and the validation set obtained by 1000 random repetitions for odd-Z nuclei and odd-N nuclei, respectively

奇Z核奇N核

训练集验证集训练集验证集

平均值 97.6% 72.3% 96.5% 67.1%

标准误差 1.7% 4.5% 2.4% 4.9%

DownLoad: CSV

[1]	Yordanov D T, Kowalska M, Blaum K, Rydt M D, Flanagan K T, Lievens P, Neugart R, Neyens G, Stroke H H 2007 Phys. Rev. Lett. 99 212501 Google Scholar
[2]	Smirnova N, Bally B, Heyde K, Nowacki F, Sieja K 2010 Phys. Lett. B 686 109 Google Scholar
[3]	baglin C M 2012 Nucl. Data Sheets 113 2187 Google Scholar
[4]	Szuecs J, Johns M, Singh B 2004 Nucl. Data Sheets 102 1 Google Scholar
[5]	Singh B 2009 Nucl. Data Sheets 110 1 Google Scholar
[6]	Yang X F, Wang S J, Wilkins S G, Ruiz R F G 2023 Prog. Part. Nucl. Phys. 129 104005 Google Scholar
[7]	Carlson J A, Gandolfi S, Pederiva F, Pieper S C, Schiavilla R, Schmidt K E, Wiringa R B 2015 Rev. Mod. Phys. 87 1067 Google Scholar
[8]	Dickhoff W, Barbieri C 2004 Prog. Part. Nucl. Phys. 52 377 Google Scholar
[9]	Hagen G, Papenbrock T, Hjorth-Jensen M, Dean D J 2014 Rep. Prog. Phys. 77 096302 Google Scholar
[10]	Lee D 2009 Prog. Part. Nucl. Phys. 63 117 Google Scholar
[11]	Caurier E, Martínez-Pinedo G, Nowacki F, Poves A, Zuker A P 2005 Rev. Mod. Phys. 77 427 Google Scholar
[12]	Bender M, Heenen P H, Reinhard P G 2003 Rev. Mod. Phys. 75 121 Google Scholar
[13]	Ring P 1996 Prog. Part. Nucl. Phys. 37 193 Google Scholar
[14]	Meng J, Toki H, Zhou S G, Zhang S Q, Long W H, Geng L S 2006 Prog. Part. Nucl. Phys. 57 470 Google Scholar
[15]	Meng J 2016 Relativistic Density Functional for Nuclear Structure (Singapore: World Scientific) pp305–354
[16]	Shen S, Liang H, Long W H, Meng J, Ring P 2019 Prog. Part. Nucl. Phys. 109 103713 Google Scholar
[17]	Goriely S, Chamel N, Pearson J 2016 Phys. Rev. C 93 034337 Google Scholar
[18]	Xia X, Lim Y, Zhao P, et al. 2018 At. Data Nucl. Data Tables 121 1 Google Scholar
[19]	Möller P, Mumpower M R, Kawano T, Myers W D 2019 At. Data Nucl. Data Tables 125 1 Google Scholar
[20]	Benediktsson J, Swain P, Ersoy O 1990 IEEE Trans. Geosci. Remote Sens. 28 540 Google Scholar
[21]	Boehnlein A, Diefenthaler M, Sato N, Schram M, Ziegler V, Fanelli C, Hjorth-Jensen M, Horn T, Kuchera M P, Lee D, Nazarewicz W, Ostroumov P, Orginos K, Poon A, Wang X N, Scheinker A, Smith M S, Pang L G 2022 Rev. Mod. Phys. 94 031003 Google Scholar
[22]	Wu X H 2023 Front. Phys. 11 1061042 Google Scholar
[23]	Niu Z M, Liang H Z 2022 Phys. Rev. C 106 L021303 Google Scholar
[24]	Ming X C, Zhang H F, Xu R R, Sun X D, Tian Y, Ge Z G 2022 Nucl. Sci. Tech. 33 48 Google Scholar
[25]	Shou R, Yin X, Ma C, Lin M, Zhao Y 2022 Phys. Rev. C 106 L061304 Google Scholar
[26]	Gao Z P, Wang Y J, Lü H L, Li Q F, Shen C W, Liu L 2021 Nucl. Sci. Tech. 32 109 Google Scholar
[27]	Neufcourt L, Cao Y, Giuliani S, Nazarewicz W, Olsen E, Tarasov O B 2020 Phys. Rev. C 101 014319 Google Scholar
[28]	Neufcourt L, Cao Y, Nazarewicz W, et al. 2018 Phys. Rev. C 98 034318 Google Scholar
[29]	Rodríguez U B, Vargas C Z, Gonçalves M, Duarte S B, Guzmán F 2019 J. Phys. G: Nucl. Part. Phys. 46 115109 Google Scholar
[30]	Rodríguez U B, Vargas C Z, Gonçalves M, Duarte S B, Guzmán F 2019 Europhys. Lett. 127 42001 Google Scholar
[31]	Utama R, Piekarewicz J, Prosper H 2016 Phys. Rev. C 93 014311 Google Scholar
[32]	Bayram T, Akkoyun S, Kara S O 2014 Ann. Nucl. Energy 63 172 Google Scholar
[33]	Gazula S, Clark J, Bohr H 1992 Nucl. Phys. A 540 1 Google Scholar
[34]	Gernoth K, Clark J, Prater J, Bohr H 1993 Phys. Lett. B 300 1 Google Scholar
[35]	Niu Z, Liang H 2018 Phys. Lett. B 778 48 Google Scholar
[36]	Athanassopoulos S, Mavrommatis E, Gernoth K, Clark J W 2004 Nucl. Phys. A 743 222 Google Scholar
[37]	Clark J W, Li H 2006 Int. J. Mod. Phys. B 20 5015 Google Scholar
[38]	Niu Z M, Fang J Y, Niu Y F 2019 Phys. Rev. C 100 054311 Google Scholar
[39]	Dong X X, An R, Lu J X, Geng L S 2023 Phys. Lett. B 838 137726 Google Scholar
[40]	Dong X X, An R, Lu J X, Geng L S 2022 Phys. Rev. C 105 014308 Google Scholar
[41]	Ma J Q, Zhang Z H 2022 Chin. Phys. C 46 074105 Google Scholar
[42]	Ma Y, Su C, Liu J, Ren Z, Xu C, Gao Y 2020 Phys. Rev. C 101 014304 Google Scholar
[43]	Wu D, Bai C, Sagawa H, Zhang H 2020 Phys. Rev. C 102 054323 Google Scholar
[44]	Utama R, Chen W C, Piekarewicz J 2016 J. Phys. G: Nucl. Part. Phys. 43 114002 Google Scholar
[45]	Akkoyun S, Bayram T, Kara S O, Sinan A 2013 J. Phys. G: Nucl. Part. Phys. 40 055106 Google Scholar
[46]	Yuan Z, Tian D, Li J, Niu Z 2021 Chin. Phys. C 45 124107 Google Scholar
[47]	Clark J W, Gernoth K A, Dittmar S, Ristig M 1999 Phys. Rev. E 59 6161 Google Scholar
[48]	Gernoth K A, Clark J W 1995 Neural Networks 8 291 Google Scholar
[49]	Shang T S, Li J, Niu Z M 2022 Nucl. Sci. Tech. 33 153 Google Scholar
[50]	Yang Z X, Fan X H, Naito T, Niu Z, Li Z P, Liang H 2022 arXiv: 2205.15649[nucl-th]
[51]	Yang Z X, Fan X H, Yin P, Zuo W 2021 Phys. Lett. B 823 136650 Google Scholar
[52]	Costiris N, Mavrommatis E, Gernoth K A, Clark J W 2009 Phys. Rev. C 80 044332 Google Scholar
[53]	Wang Y, Zhang X, Niu Z, Li Z 2022 Phys. Lett. B 830 137154 Google Scholar
[54]	Akkoyun S, Kaya H, Torun Y 2022 Indian J. Phys. 96 1791 Google Scholar
[55]	Lasseri R D, Regnier D, Ebran J P, Penon A 2020 Phys. Rev. Lett. 124 162502 Google Scholar
[56]	Akkoyun S, Laouet N, Benrachi F 2020 arXiv: 2001.08561[nucl-th]
[57]	Ma N N, Zhao T L, Wang W X, Zhang H F 2023 Phys. Rev. C 107 014310 Google Scholar
[58]	Li C Q, Tong C N, Du H J, Pang L G 2022 Phys. Rev. C 105 064306 Google Scholar
[59]	Yuan Z, Bai D, Ren Z, Wang Z 2022 Chin. Phys. C 46 024101 Google Scholar
[60]	Kwon M, Oh Y, Song Y H, et al. 2021 New Physics: Sae Mulli 71 599 Google Scholar
[61]	Zhang X, Lin W, Yao J M, Jiao C F, Romero A M, Rodríguez T R, Hergert H 2023 Phys. Rev. C 107 024304 Google Scholar
[62]	Munoz J M, Akkoyun S, Reyes Z P, Pachon L A 2023 Phys. Rev. C 107 034308 Google Scholar
[63]	Niu Z, Liang H, Sun B, et al. 2019 Phys. Rev. C 99 064307 Google Scholar
[64]	Costiris N, Mavrommatis E, Gernoth K, Clark J, Li H 2008 arXiv: 0809.0383[nucl-th]
[65]	Akkoyun S, Amrani N, Bayram T 2023 Appl. Radiat. Isot. 191 110554 Google Scholar
[66]	Huang T X, Wu X H, Zhao P W 2022 Commun. Theor. Phys. 74 095302 Google Scholar
[67]	Ma C W, Wei X B, Chen X X, Peng D, Wang Y T, Pu J, Cheng K X, Guo Y F, Wei H L 2022 Chin. Phys. C 46 074104 Google Scholar
[68]	Peng D, Wei H L, Chen X X, Wei X B, Wang Y T, Pu J, Cheng K X, Ma C W 2022 J. Phys. G: Nucl. Part. Phys. 49 085102 Google Scholar
[69]	Ma C W, Peng D, Wei H L, Niu Z M, Wang Y T, Wada R 2020 Chin. Phys. C 44 014104 Google Scholar
[70]	Ma C W, Peng D, Wei H L, Wang Y T, Pu J 2020 Chin. Phys. C 44 124107 Google Scholar
[71]	Ma C W, Wei H L, Liu X Q, Su J, Zheng H, Lin W P, Zhang Y X 2021 Prog. Part. Nucl. Phys. 121 103911 Google Scholar
[72]	Yesilkanat C M, Akkoyun S 2023 J. Phys. G: Nucl. Part. Phys. 50 055101 Google Scholar
[73]	Akkoyun S, Bayram T 2014 Int. J. Mod. Phys. E 23 1450064 Google Scholar
[74]	Wang X, Zhu L, Su J 2021 Phys. Rev. C 104 034317 Google Scholar
[75]	Wu D, Bai C, Sagawa H, Nishimura S, Zhang H 2021 Phys. Rev. C 104 054303 Google Scholar
[76]	Wu X, Ren Z, Zhao P, et al. 2022 Phys. Rev. C 105 L031303 Google Scholar
[77]	Alhassan E, Rochman D, Vasiliev A, Hursin M, Koning A J, Ferroukhi H 2022 Nucl. Sci. Tech. 33 50 Google Scholar
[78]	Möller P, Nix J R 1990 Nucl. Phys. A 520 c369 Google Scholar
[79]	Breiman L 2001 Mach. Learn. 45 5 Google Scholar
[80]	Chen T, Guestrin C 2016 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining San Francisco, USA, August 13–17, 2016 p785
[81]	Carnini M, Pastore A 2020 J. Phys. G: Nucl. Part. Phys. 47 082001 Google Scholar
[82]	Maderna C, Soardi P M 1985 Lezioni di analisi matematica (Torino: Città Studi Edizioni) pp1–354
[83]	Pedregosa F, Varoquaux G, Gramfort A, et al. 2011 J. Mach. Learn. Res. 12 2825 Google Scholar
[84]	From ENSDF database as of 5.16, 2019. Version available at http://www.nndc.bnl.gov/ensarchivals/[2019-5-16]
[85]	Wraith C, Yang X, Xie L, Babcock C, Bieroń J, Billowes J, Bissell M, Blaum K, Cheal B, Filippin L, Garcia Ruiz R, Gins W, Grob L, Gaigalas G, Godefroid M, Gorges C, Heylen H, Honma M, Jönsson P, Kaufmann S, Kowalska M, Krämer J, Malbrunot-Ettenauer S, Neugart R, Neyens G, Nörtershäuser W, Nowacki F, Otsuka T, Papuga J, Sánchez R, Tsunoda Y, Yordanov D 2017 Phys. Lett. B 771 385 Google Scholar

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Vol. 72, Issue 15 - 2023-08-05

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Prediction of ground-state spin in odd-A nuclei within decision tree

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Corresponding author: Li Jian, jianli@jlu.edu.cn ; Yang Dong, dyang@jlu.edu.cn ;

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	奇Z核		奇N核
	训练集	验证集	训练集	验证集
平均值	97.6%	72.3%	96.5%	67.1%
标准误差	1.7%	4.5%	2.4%	4.9%

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Prediction of ground-state spin in odd-A nuclei within decision tree

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