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Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon

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Abstract

Within a transport model, we investigated the effects of the momentum dependence of the nuclear symmetry potential on the pion observables in central Sn + Sn collisions at 270 MeV/nucleon. To this end, the quantity \(U_\text {sym}^{\infty }(\rho _{0})\) (i.e., the value of the nuclear symmetry potential at the saturation density \(\rho _{0}\) and infinitely large nucleon momentum) was used to characterize the momentum dependence of the nuclear symmetry potential. With a certain L (i.e., the slope of the nuclear symmetry energy at \(\rho _{0}\)), the characteristic parameter \(U_\text {sym}^{\infty }(\rho _{0})\) of the symmetry potential significantly affects the production of \(\pi ^{-}\) and \(\pi ^{+}\) and their pion ratios. Moreover, by comparing the charged pion yields, pion ratios, and spectral pion ratios of the theoretical simulations for the reactions \(^{108}\)Sn + \(^{112}\)Sn and \(^{132}\)Sn + \(^{124}\)Sn with the corresponding data in the S\(\pi \)RIT experiments, we found that our results favor a constraint on \(U_\text {sym}^{\infty }(\rho _{0})\) (i.e., \(-160^{+18}_{-9}\) MeV), and L is also suggested within a range of 62.7 MeV\(<L<93.1\) MeV. In addition, the pion observable for \(^{197}\)Au + \(^{197}\)Au collisions at 400 MeV/nucleon also supports the extracted value for \(U_\text {sym}^{\infty }(\rho _{0})\).

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Notes

  1. Approximately at \(t=13\) fm/c, the reaction approaches maximum compression, the nucleons in compression region are naturally in dense but low-energy phase.

  2. The value of 81 MeV is the transition kinetic energy for the symmetry potential at \(1.5\rho _{0}\) with \(L=62.7\) MeV and \(U_\text {sym}^{\infty }(\rho _{0})=-240\) MeV.

References

  1. S. Typel, B.A. Brown, Neutron radii and the neutron equation of state in relativistic models. Phys. Rev. C 64, 027302 (2001). https://doi.org/10.1103/PhysRevC.64.027302

    Article  ADS  Google Scholar 

  2. E.E. Kolomeitsev, C. Hartnack, H.W. Barz et al., Transport theories for heavy-ion collisions in the 1 A GeV regime. J. Phys. G Nucl. Part. Phys. 31, S741 (2005). https://doi.org/10.1088/0954-3899/31/6/015

    Article  Google Scholar 

  3. V. Baran, M. Colonna, V. Greco et al., Reaction dynamics with exotic nuclei. Phys. Rep. 410, 335 (2005). https://doi.org/10.1016/j.physrep.2004.12.004

    Article  ADS  Google Scholar 

  4. B.A. Li, L.W. Chen, C.M. Ko, Recent progress and new challenges in isospin physics with heavy-ion reactions. Phys. Rep. 464, 113 (2008). https://doi.org/10.1016/j.physrep.2008.04.005

    Article  ADS  Google Scholar 

  5. A. Tamii, I. Poltoratska, P. vonNeumann-Cosel et al., Complete electric dipole response and the neutron skin in \(^{208}\)Pb. Phys. Rev. Lett. 107, 062502 (2011). https://doi.org/10.1103/PhysRevLett.107.062502

    Article  ADS  Google Scholar 

  6. X. Viñas, M. Centelles, X. Roca-Maza et al., Density dependence of the symmetry energy from neutron skin thickness in finite nuclei. Eur. Phys. J. A 50, 27 (2014). https://doi.org/10.1140/epja/i2014-14027-8

    Article  ADS  Google Scholar 

  7. C.J. Horowitz, E.F. Brown, Y. Kim et al., A way forward in the study of the symmetry energy: experiment, theory, and observation. J. Phys. G Nucl. Part. Phys. 41, 093001 (2014). https://doi.org/10.1088/0954-3899/41/9/093001

    Article  ADS  Google Scholar 

  8. P.G. Reinhard, W. Nazarewicz, Nuclear charge and neutron radii and nuclear matter: trend analysis in Skyrme density-functional-theory approach. Phys. Rev. C 93, 051303 (2016). https://doi.org/10.1103/PhysRevC.93.051303

    Article  ADS  Google Scholar 

  9. M. Baldo, G.F. Burgio, The nuclear symmetry energy. Prog. Part. Nucl. Phys. 91, 203 (2016). https://doi.org/10.1016/j.ppnp.2016.06.006

    Article  ADS  Google Scholar 

  10. C.W. Ma, Y.G. Ma, Shannon information entropy in heavy-ion collisions. Prog. Part. Nucl. Phys. 99, 120 (2018). https://doi.org/10.1016/j.ppnp.2018.01.002

    Article  ADS  Google Scholar 

  11. H. Yu, D.Q. Fang, Y.G. Ma, Investigation of the symmetry energy of nuclear matter using isospin-dependent quantum molecular dynamics. Nucl. Sci. Tech. 31, 61 (2020). https://doi.org/10.1007/s41365-020-00766-x

    Article  Google Scholar 

  12. C.W. Ma, H.L. Wei, X.Q. Liu et al., Nuclear fragments in projectile fragmentation reactions. Prog. Part. Nucl. Phys. 121, 103911 (2021). https://doi.org/10.1016/j.ppnp.2021.103911

    Article  Google Scholar 

  13. J. Estee, W.G. Lynch, C.Y. Tsang et al., Probing the symmetry energy with the spectral pion ratio. Phys. Rev. Lett. 126, 162701 (2021). https://doi.org/10.1103/PhysRevLett.126.162701

    Article  ADS  Google Scholar 

  14. C.Y. Tsang, M.B. Tsang, P. Danielewicz et al., Insights on Skyrme parameters from GW170817. Phys. Lett. B 796, 1 (2019). https://doi.org/10.1016/j.physletb.2019.05.055

    Article  ADS  MathSciNet  Google Scholar 

  15. Y. Lim, J.W. Holt, Neutron star tidal deformabilities constrained by nuclear theory and experiment. Phys. Rev. Lett. 121, 062701 (2018). https://doi.org/10.1103/PhysRevLett.121.062701

    Article  ADS  Google Scholar 

  16. I. Tews, J. Margueron, S. Reddy, Critical examination of constraints on the equation of state of dense matter obtained from GW170817. Phys. Rev. C 98, 045804 (2018). https://doi.org/10.1103/PhysRevC.98.045804

    Article  ADS  Google Scholar 

  17. A. Drago, A. Lavagno, G. Pagliara et al., Early appearance of \(\Delta \) isobars in neutron stars. Phys. Rev. C 90, 065809 (2014). https://doi.org/10.1103/PhysRevC.90.065809

    Article  ADS  Google Scholar 

  18. A.W. Steiner, S. Gandolfi, Connecting neutron star observations to three-body forces in neutron matter and to the nuclear symmetry energy. Phys. Rev. Lett. 108, 081102 (2012). https://doi.org/10.1103/PhysRevLett.108.081102

    Article  ADS  Google Scholar 

  19. C. Ducoin, J. Margueron, C. Providência et al., Core-crust transition in neutron stars: Predictivity of density developments. Phys. Rev. C 83, 045810 (2011). https://doi.org/10.1103/PhysRevC.83.045810

    Article  ADS  Google Scholar 

  20. J.M. Lattimer, M. Prakash, The equation of state of hot, dense matter and neutron stars. Phys. Rep. 621, 127 (2016). https://doi.org/10.1016/j.physrep.2015.12.005

    Article  ADS  MathSciNet  Google Scholar 

  21. B.A. Brown, Constraints on the Skyrme equations of state from properties of doubly magic nuclei. Phys. Rev. Lett. 111, 232502 (2013). https://doi.org/10.1103/PhysRevLett.111.232502

    Article  ADS  Google Scholar 

  22. B.A. Li, B.J. Cai, L.W. Chen et al., Isospin dependence of nucleon effective masses in neutron-rich matter. Nucl. Sci. Tech. 27, 141 (2016). https://doi.org/10.1007/s41365-016-0140-4

    Article  Google Scholar 

  23. P. Danielewicz, R. Lacey, W.G. Lynch, Determination of the equation of state of dense matter. Science 298, 1592 (2002). https://doi.org/10.1126/science.1078070

    Article  ADS  Google Scholar 

  24. M. Oertel, M. Hempel, T. Klahn et al., Equations of state for supernovae and compact stars. Rev. Mod. Phys. 89, 015007 (2017). https://doi.org/10.1103/RevModPhys.89.015007

    Article  ADS  Google Scholar 

  25. B.J. Cai, L.W. Chen, Constraints on the skewness coefficient of symmetric nuclear matter within the nonlinear relativistic mean field model. Nucl. Sci. Tech. 28, 185 (2017). https://doi.org/10.1007/s41365-017-0329-1

    Article  Google Scholar 

  26. G.F. Wei, Q.J. Zhi, X.W. Cao et al., Examination of an isospin-dependent single-nucleon momentum distribution for isospin-asymmetric nuclear matter in heavy-ion collisions. Nucl. Sci. Tech. 31, 71 (2020). https://doi.org/10.1007/s41365-020-00779-6

    Article  Google Scholar 

  27. J. Liu, C. Gao, N. Wan et al., Basic quantities of the equation of state in isospin asymmetric nuclear matter. Nucl. Sci. Tech. 32, 117 (2021). https://doi.org/10.1007/s41365-021-00955-2

    Article  Google Scholar 

  28. G.W. Hoffmann, W.R. Coker, Coupled-channel calculations of the energy dependence of the (\(p\),\(n\)) charge-exchange reaction. Phys. Rev. Lett. 29, 227 (1972). https://doi.org/10.1103/PhysRevLett.29.227

    Article  ADS  Google Scholar 

  29. A.J. Koning, J.P. Delaroche, Local and global nucleon optical models from 1 KeV to 200 MeV. Nucl. Phys. A 713, 231 (2003). https://doi.org/10.1016/S0375-9474(02)01321-0

    Article  ADS  Google Scholar 

  30. J.P. Jeukenne, C. Mahaux, R. Sartor, Dependence of the Fermi energy upon neutron excess. Phys. Rev. C 43, 2211 (1991). https://doi.org/10.1103/PhysRevC.43.2211

    Article  ADS  Google Scholar 

  31. G. Jhang, J. Estee, J. Barney et al., Symmetry energy investigation with pion production from Sn+Sn systems. Phys. Lett. B 813, 136016 (2021). https://doi.org/10.1016/j.physletb.2020.136016

    Article  Google Scholar 

  32. R. Shane, A.B. McIntosh, T. Isobe et al., S\(\pi \)RIT: a time-projection chamber for symmetry-energy studies. Nucl. Instr. Meth. A 784, 513 (2015). https://doi.org/10.1016/j.nima.2015.01.026

    Article  ADS  Google Scholar 

  33. W. Reisdorf, A. Andronic, R. Averbeck et al., Systematics of central heavy ion collisions in the regime. Nucl. Phys. A 848, 366 (2010). https://doi.org/10.1016/j.nuclphysa.2010.09.008

    Article  ADS  Google Scholar 

  34. G.C. Yong, Symmetry energy extracted from the S\(\pi \)RIT pion data in Sn + Sn systems. Phys. Rev. C 104, 014613 (2021). https://doi.org/10.1103/PhysRevC.104.014613

    Article  ADS  Google Scholar 

  35. R. Subedi, R. Shneor, P. Monaghan et al., Probing cold dense nuclear matter. Science 320, 1476 (2008). https://doi.org/10.1126/science.1156675

    Article  ADS  Google Scholar 

  36. L.B. Weinstein, E. Piasetzky, D.W. Higinbotham et al., Short range correlations and the EMC effect. Phys. Rev. Lett. 106, 052301 (2011). https://doi.org/10.1103/PhysRevLett.106.052301

    Article  ADS  Google Scholar 

  37. M.M. Sargsian, New properties of the high-momentum distribution of nucleons in asymmetric nuclei. Phys. Rev. C 89, 034305 (2014). https://doi.org/10.1103/PhysRevC.89.034305

    Article  ADS  Google Scholar 

  38. C.C. Degli Atti, In-medium short-range dynamics of nucleons: recent theoretical and experimental advances. Phys. Rep. 590, 1 (2015). https://doi.org/10.1016/j.physrep.2015.06.002

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. O. Hen, M. Sargsian, L.B. Weinstein et al., Momentum sharing in imbalanced Fermi systems. Science 346, 614 (2014). https://doi.org/10.1126/science.1256785

    Article  ADS  Google Scholar 

  40. M. Duer, O. Hen, E. Piasetzky et al., Probing high-momentum protons and neutrons in neutron-rich nuclei. Nature 560, 617 (2018). https://doi.org/10.1038/s41586-018-0400-z

    Article  Google Scholar 

  41. K.A. Brueckner, J. Dabrowski, Symmetry energy and the isotopic spin dependence of the single-particle potential in nuclear matter. Phys. Rev. 134, B722 (1964). https://doi.org/10.1103/PhysRev.134.B722

    Article  ADS  Google Scholar 

  42. J. Dabrowski, P. Haensel, Spin and spin-isospin symmetry energy of nuclear matter. Phys. Rev. C 7, 916 (1973). https://doi.org/10.1103/PhysRevC.7.916

    Article  ADS  Google Scholar 

  43. V. Giordano, M. Colonna, M.D. Toro et al., Isospin emission and flow at high baryon density: a test of the symmetry potential. Phys. Rev. C 81, 044611 (2010). https://doi.org/10.1103/PhysRevC.81.044611

    Article  ADS  Google Scholar 

  44. J. Xu, L.W. Chen, M.B. Tsang et al., Understanding transport simulations of heavy-ion collisions at 100 A and 400 A MeV: comparison of heavy-ion transport codes under controlled conditions. Phys. Rev. C 93, 044609 (2016). https://doi.org/10.1103/PhysRevC.93.044609

    Article  ADS  Google Scholar 

  45. Y.X. Zhang, Y.J. Wang, M. Colonna et al., Comparison of heavy-ion transport simulations: collision integral in a box. Phys. Rev. C 97, 034625 (2018). https://doi.org/10.1103/PhysRevC.97.034625

    Article  ADS  Google Scholar 

  46. A. Ono, J. Xu, M. Colonna et al., Comparison of heavy-ion transport simulations: collision integral with pions and \(\Delta \) resonances in a box. Phys. Rev. C 100, 044617 (2019). https://doi.org/10.1103/PhysRevC.100.044617

    Article  ADS  Google Scholar 

  47. M. Colonna, Y.X. Zhang, Y.J. Wang et al., Comparison of heavy-ion transport simulations: mean-field dynamics in a box. Phys. Rev. C 104, 024603 (2021). https://doi.org/10.1103/PhysRevC.104.024603

    Article  ADS  Google Scholar 

  48. H. Wolter, M. Colonna, D. Cozma et al., Transport model comparison studies of intermediate-energy heavy-ion collisions. Prog. Part. Nucl. Phys. 125, 103962 (2022). https://doi.org/10.1016/j.ppnp.2022.103962

    Article  Google Scholar 

  49. C.B. Das, S. Das Gupta, C. Gale et al., Momentum dependence of symmetry potential in asymmetric nuclear matter for transport model calculations. Phys. Rev. C 67, 034611 (2003). https://doi.org/10.1103/PhysRevC.67.034611

    Article  ADS  Google Scholar 

  50. B.A. Li, C.B. Das, S. Das Gupta et al., Momentum dependence of the symmetry potential and nuclear reactions induced by neutron-rich nuclei at RIA. Phys. Rev. C 69, 011603 (2004). https://doi.org/10.1103/PhysRevC.69.011603

    Article  ADS  Google Scholar 

  51. L.W. Chen, B.A. Li, A note of an improved MDI interaction for transport model simulations of heavy ion collisions (Unpublished, Texas A &M University-Commerce, 2010)

    Google Scholar 

  52. C. Xu, B.A. Li, Improved single particle potential for transport model simulations of nuclear reactions induced by rare isotope beams. Phys. Rev. C 81, 044603 (2010). https://doi.org/10.1103/PhysRevC.81.044603

    Article  ADS  Google Scholar 

  53. L.W. Chen, C.M. Ko, B.A. Li et al., Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter. Eur. Phys. J. A 50, 29 (2014). https://doi.org/10.1140/epja/i2014-14029-6

    Article  ADS  Google Scholar 

  54. G.F. Wei, C. Xu, W. Xie et al., Effects of density-dependent scenarios of in-medium nucleon-nucleon interactions in heavy-ion collisions. Phys. Rev. C 102, 024614 (2020). https://doi.org/10.1103/PhysRevC.102.024614

    Article  ADS  Google Scholar 

  55. J. Dechargé, D. Gogny, Hartree-fock-bogolyubov calculations with the D1 effective interaction on spherical nuclei. Phys. Rev. C 21, 1568 (1980). https://doi.org/10.1103/PhysRevC.21.1568

    Article  ADS  Google Scholar 

  56. T. Duguet, P. Bonche, Density dependence of two-body interactions for beyond-mean-field calculations. Phys. Rev. C 67, 054308 (2003). https://doi.org/10.1103/PhysRevC.67.054308

    Article  ADS  Google Scholar 

  57. J.W. Negele, Structure of finite nuclei in the local-density approximation. Phys. Rev. C 1, 1260 (1970). https://doi.org/10.1103/PhysRevC.1.1260

    Article  ADS  Google Scholar 

  58. J. Xu, L.W. Chen, B.A. Li, Thermal properties of asymmetric nuclear matter with an improved isospin- and momentum-dependent interaction. Phys. Rev. C 91, 014611 (2015). https://doi.org/10.1103/PhysRevC.91.014611

    Article  ADS  Google Scholar 

  59. H.Y. Kong, Y. Xia, J. Xu et al., Reexamination of the neutron-to-proton-ratio puzzle in intermediate-energy heavy-ion collisions. Phys. Rev. C 91, 047601 (2015). https://doi.org/10.1103/PhysRevC.91.047601

    Article  ADS  Google Scholar 

  60. H.Y. Kong, J. Xu, L.W. Chen et al., Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances using a dynamical approach. Phys. Rev. C 95, 034324 (2017). https://doi.org/10.1103/PhysRevC.95.034324

    Article  ADS  Google Scholar 

  61. S. Hama, B.C. Clark, E.D. Cooper et al., Global Dirac optical potentials for elastic proton scattering from heavy nuclei. Phys. Rev. C 41, 2737 (1990). https://doi.org/10.1103/PhysRevC.41.2737

    Article  ADS  Google Scholar 

  62. O. Buss, T. Gaitanos, K. Gallmeister et al., Transport-theoretical description of nuclear reactions. Phys. Rep. 512, 1 (2012). https://doi.org/10.1016/j.physrep.2011.12.001

    Article  ADS  Google Scholar 

  63. M. Ericson, T.E.O. Ericson, Optical properties of low-energy pions in nuclei. Ann. Phys. 36, 323 (1966). https://doi.org/10.1016/0003-4916(66)90302-2

    Article  ADS  MATH  Google Scholar 

  64. C. García-Recio, E. Oset, L.L. Salcedo, S-wave optical potential in pionic atoms. Phys. Rev. C 37, 194 (1988). https://doi.org/10.1103/PhysRevC.37.194

    Article  ADS  Google Scholar 

  65. J. Nieves, E. Oset, C. García-Recio, Many-body approach to low-energy pion-nucleus scattering. Nucl. Phys. A 554, 554 (1993). https://doi.org/10.1016/0375-9474(93)90246-T

    Article  ADS  Google Scholar 

  66. Z. Zhang, C.M. Ko, Medium effects on pion production in heavy ion collisions. Phys. Rev. C 95, 064604 (2017). https://doi.org/10.1103/PhysRevC.95.064604

    Article  ADS  Google Scholar 

  67. G.F. Wei, C. Liu, X.W. Cao et al., Necessity of self-consistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions. Phys. Rev. C 103, 054607 (2021). https://doi.org/10.1103/PhysRevC.103.054607

    Article  ADS  Google Scholar 

  68. G.F. Wei, B.A. Li, G.C. Yong et al., Effects of retarded electrical fields on observables sensitive to the high-density behavior of the nuclear symmetry energy in heavy-ion collisions at intermediate energies. Phys. Rev. C 97, 034620 (2018). https://doi.org/10.1103/PhysRevC.97.034620

    Article  ADS  Google Scholar 

  69. G.F. Wei, G.C. Yong, L. Ou et al., Beam-energy dependence of the relativistic retardation effects of electrical fields on the \(\pi ^{-}/\pi ^{+}\) ratio in heavy-ion collisions. Phys. Rev. C 98, 024618 (2018). https://doi.org/10.1103/PhysRevC.98.024618

    Article  ADS  Google Scholar 

  70. B.A. Li, G.C. Yong, W. Zuo, Near-threshold pion production with radioactive beams. Phys. Rev. C 71, 014608 (2005). https://doi.org/10.1103/PhysRevC.71.014608

    Article  ADS  Google Scholar 

  71. P. Danielewicz, P. Singh, J. Lee, Symmetry energy III: Isovector skins. Nucl. Phys. A 958, 147 (2017). https://doi.org/10.1016/j.nuclphysa.2016.11.008

    Article  ADS  Google Scholar 

  72. M.D. Cozma, Feasibility of constraining the curvature parameter of the symmetry energy using elliptic flow data. Eur. Phys. J. A 54, 40 (2018). https://doi.org/10.1140/epja/i2018-12470-1

    Article  ADS  Google Scholar 

  73. Z. Zhang, C.M. Ko, Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter. Phys. Rev. C 97, 014610 (2018). https://doi.org/10.1103/PhysRevC.97.014610

    Article  ADS  Google Scholar 

  74. J.R. Stone, P. Danielewicz, Y. Iwata, Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions. Phys. Rev. C 96, 014612 (2017). https://doi.org/10.1103/PhysRevC.96.014612

    Article  ADS  Google Scholar 

  75. P. Russotto, S. Gannon, S. Kupny et al., Results of the ASY-EOS experiment at GSI: the symmetry energy at suprasaturation density. Phys. Rev. C 94, 034608 (2016). https://doi.org/10.1103/PhysRevC.94.034608

    Article  ADS  Google Scholar 

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Acknowledgements

Gao-Feng Wei would like to thank Profs. Bao-An Li and Gao-Chan Yong for their helpful discussions.

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Authors and Affiliations

  1. School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550025, China

    Gao-Feng Wei, Xin Huang, Qi-Jun Zhi & Ai-Jun Dong

  2. Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University, Guiyang, 550025, China

    Gao-Feng Wei, Qi-Jun Zhi & Ai-Jun Dong

  3. Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang, 550025, China

    Chang-Gen Peng

  4. College of Physics, Guizhou University, Guiyang, 550025, China

    Zheng-Wen Long

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  1. Gao-Feng Wei
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Gao-Feng Wei, Xin Huang and Qi-Jun Zhi. The first draft of the manuscript was written by Gao-Feng Wei, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Gao-Feng Wei.

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This work was supported by the National Natural Science Foundation of China (Nos. 11965008 and 11405128), the Guizhou Provincial Science and Technology Foundation (No. [2020]1Y034), and the PhD-funded project of Guizhou Normal University (No. GZNUD[2018]11).

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Wei, GF., Huang, X., Zhi, QJ. et al. Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon. NUCL SCI TECH 33, 163 (2022). https://doi.org/10.1007/s41365-022-01146-3

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