KLEIN–GORDON EQUATION, QUNTUM RELATIVISTIC HYDRODYNAMICS AND QUANTUM SHOCK WAVES IN DESCRIBING COLLISIONS OF ATOMIC NUCLEI

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Дәйексөз келтіру

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Аннотация

In this work, the equations of quantum relativistic hydrodynamics are obtained from the effective Klein–Fock–Gordon equation taking into account dissipation. Taking into account dissipation in the Klein–Gordon equation leads to the need to introduce an additional thermal term and an equation for it. As a result, a closed system of equations was obtained taking into account non-equilibrium processes, which makes it possible to describe the dynamics of the process of collisions of atomic nuclei and calculate the yield of secondary particles. Solving the resulting equations makes it possible to identify quantum shock waves and the time evolution of the resulting hot spot. The calculated spectra of emitted protons in heavy ion collisions are compared with available experimental data.

Авторлар туралы

A. D’yachenko

NRC “Kurchatov Institute” — PNPI; Emperor Alexander I Petersburg State Transport University

Email: dyachenko_a@mail.ru
Gatchina, Russia; St. Petersburg, Russia

Әдебиет тізімі

  1. O. Klein, Z. Phys. 37, 895 (1926).
  2. V. Fock, Z. Phys. 38, 242 (1926).
  3. W. Gordon, Z. Phys. 40, 117 (1926).
  4. E. Madelung, Z. Phys. 40, 332 (1926).
  5. С.-Y. Wong, J. Math. Phys. 51, 122304 (2010); arXiv: 1011.5510 [hep-ph].
  6. C.-K. Lin and K.-C. Wu, J. Math. Pures. Appl. 98, 328 (2012).
  7. А. Т. Дьяченко, ЯФ 86, 428 (2023) [Phys. At. Nucl. 86, 289 (2023)].
  8. A. H. Taub, Phys. Rev. 74, 328 (1948).
  9. L. D. Landau, Izv. Akad. Nauk SSSR. Ser. Fiz. 17, 51 (1953) [Collected papers of L. D. Landau, Ed. by D. Ter-Haar (Pergamon Press, Oxford, 1965), Paper no. 74].
  10. С. З. Беленький, Л. Д. Ландау, УФН 56, 309 (1955).
  11. S. Z. Belenkij and L. D. Landau, Nuovo Cimento Suppl. 3, 15 (1956).
  12. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987).
  13. H. Stocker and W. Greiner, Phys. Rept. 137, 277 (1986).
  14. A. T. D’yachenko, K. A. Gridnev, and W. Greiner, J. Phys. G 40, 085101 (2013).
  15. A. T. D’yachenko and I. A. Mitropolsky, Phys. At. Nucl. 83, 558 (2020).
  16. A. T. D’yachenko and I. A. Mitropolsky, Phys. At. Nucl. 85, 1053 (2023).
  17. A. T. D’yachenko and I. A. Mitropolsky, Phys. Part. Nucl. 53, 505 (2022).
  18. A. T. D’yachenko, K. A. Gridnev, and I. A. Mitropolsky, Bull. Russ. Acad. Sci.: Phys. 79, 858 (2015).
  19. A. T. D’yachenko and I. A. Mitropolsky, EPJ Web Conf. 204, 03018 (2019).
  20. A. T. D’yachenko and I. A. Mitropolsky, Phys. At. Nucl. 82, 1641 (2019).
  21. A. T. D’yachenko, and I. A. Mitropolsky, Bull. Russ. Acad. Sci.: Phys. 86, 962 (2022).
  22. J. Nemeth, М. Barranco, С. Ngo, and E. Tomasi, Z. Phys. A 323, 419 (1986).
  23. S. Nagamiya, М.-C. Lemaire, E. Moeller, S. Schnetzer, G. Shapiro, H. Steiner, and I. Tanihata, Phys. Rev. C 24, 971 (1981).
  24. И. Н. Мишустин, В. Н. Русских, Л. М. Сатаров, ЯФ 54, 429 (1991) [Sov. J. Nucl. Phys. 54, 260 (1991)].
  25. Г. А. Милехин, ЖЭТФ 35, 1185 (1958) [Sov. Рhys. JETP 35, 829 (1959)].
  26. Э. В. Шуряк, ЯФ 16, 395 (1972) [Sov. J. Nucl. Phys. 16, 220 (1972)].
  27. М. Ю. Иванов, Ю. А. Кудеяров, К. П. Станюкович, Г. Д. Ширков, ЯФ 25, 1293 (1977) [Sov. J. Nucl. Phys. 25, 685 (1977)].
  28. P. Bonche, S. Koonin, and J. W. Negele, Phys. Rev. C 13, 1226 (1976).
  29. А. Т. Дьяченко, В. А. Рубченя, В. П. Эйсмонт, Изв. АН СССР. Сер. физ. 45, 764 (1981) [Bull. Acad. Sci. USSR: Phys. 45, 81 (1981)].
  30. А. Т. Дьяченко, ЯФ 57, 2006 (1994) [Phys. At. Nucl. 57, 1930 (1994)].
  31. A. T. D’yachenko, J. Phys. G26, 861 (2000).
  32. W. Sheid, H. Muller, and W. Greiner, Phys. Rev. Lett.32, 741 (1974).
  33. J. Hofmann, H. Stoecker, U. W. Heinz, W. Scheid, and W. Greiner, Phys. Rev. Lett. 36, 88 (1976).
  34. H. G. Baumgardt, J. U. Schott, Y. Sakamoto, E. Schopper, H. Stoecker, J. Hofmann, W. Scheid, and W. Greiner, Z. Phys. A 273, 359 (1975).
  35. H. H. Gutbrod, A. M. Poskanzer, and H. G. Ritter, Rept. Prog. Phys. 52, 1267 (1989).
  36. H. H. Gutbrod, K. H. Kampert, В. Kolb, A. M. Poskanzer, H. G. Ritter, R. Schicker, and H. R. Schmidt, Phys. Rev. C 42, 640 (1990).
  37. P. Rau, J. Steinheimer, B. Betz, H. Petersen, M. Bleicher, and H. Stoecker, arXiv: 1003.1232 [nucl-th].
  38. I. Bouras, E. Molnar, H. Niemi, Z. Xu, A. El, O. Fochler, C. Greiner, and D. H. Rischke, Phys. Rev. Lett. 103, 032301 (2009).
  39. J. Adams et al. (STAR Collab.), Phys. Rev. Lett. 95, 152301 (2005).
  40. S. S. Adler et al. (PHENIX Collab.), Phys. Rev. Lett. 97, 052301 (2006).
  41. J. G. Ulery et al. (STAR Collab.), Nucl. Phys. A 774, 581 (2006).
  42. A. Adare et al. (PHENIX Collab.), Phys. Rev. C 78, 014901 (2008).
  43. L. M. Satarov, H. Stoecker, and I. N. Mishustin, Phys. Lett. B 627, 64 (2005).
  44. A. Kovalenko and A. Leonidov, Eur. Phys. J. C 82, 378 (2022).
  45. A. V. Merdeev, L. M. Satarov, and I. N. Mishustin, Phys. Rev. С 84, 014907 (2011).
  46. Yu. B. Ivanov, V. N. Russkikh, and V. D. Toneev, Phys. Rev. C 73, 044904 (2006).
  47. H. Petersen, J. Steinheimer, G. Burau, M. Bleicher, and H. Stocker, Phys. Rev. С 78, 044901 (2008).
  48. A. S. Khvorostukhin, E. E. Kolomeitsev, and V. D. Toneev, Eur. Phys. J. A 57, 294 (2021).
  49. A. V. Dementev and N. M. Sobolevsky, Nucl. Tracks Radiat. Meas. 30, 553 (1999).
  50. S. G. Mashnik, K. K. Gudima, R. E. Prael, A. J. Sierk, M. I. Baznat, and N. V. Mokhov, LAUR-08-2931 (Los Alamos, 2008), arXiv: 0805.0751 [nucl-th].
  51. S. G. Mashnik, J. S. Bull, H. G. Hughes, R. E. Prael, and A. J. Sierk, Eur. Phys. J. Plus 126, 49 (2011).
  52. T. Koi, D. H. Wright, G. Folger, V. Ivanchenko, M. Kossov, N. Starlov, A. Heikkinen, P. Truscott, F. Lei, and H. P. Wellisch, AIP Conf. Proc. 896, 21 (2007).
  53. B. M. Abramov, M. Baznat, Yu. A. Borodin, S. A. Bulychjov, I. A. Dukhovskoy, A. P. Krutenkova, V. V. Kulikov, M. A. Martemianov, M. A. Matsyuk, and E. N. Turdakina, Phys. At. Nucl. 84, 467 (2021).
  54. B. M. Abramov, P. N. Alekseev, Yu. A. Borodin, S. A. Bulychjov, I. A. Dukhovskoy, A. P. Krutenkova, V. V. Kulikov, M. A. Martemianov, M. A. Matsyuk, S. G. Mashnik, E. N. Turdakina, and A. I. Khanov, Phys. At. Nucl. 78, 373 (2015).
  55. P. J. Siemens and J. O. Rasmussen, Phys. Rev. Lett. 42, 880 (1979).
  56. J. S. Diaz and S. E. Rigby, arXiv: 2110.09488v1 [physics.flu-dyn].
  57. A. T. D’yachenko, Phys. At. Nucl. 87, 125 (2024).
  58. A. G. Afonin, M. Yu. Bogolyubsky, A. A. Volkov, D. K. Elumakhov, V. N. Zapolsky, A. A. Ivanilov, A. Yu. Kalinin, A. N. Krinitsyn, N. V. Kulagin, V. I. Kryshkin, D. I. Patalakha, K. A. Romanishin, V. V. Skvortsov, V. V. Talov, L. K. Turchanovich, and Yu. A. Chesnokov, Phys. At. Nucl. 83, 228 (2020).
  59. O. Panova, A. Motornenko, M. I. Gorenstein, J. Steinheimer, and H. Stoecker, Phys. Rev. C 100, 054617 (2019).
  60. A. Bulgac, Y.-L. Luo, and K. J. Roche, Phys. Rev. Lett. 108, 150401 (2012).
  61. L. Salasnich, Eur. Phys. Lett. 96, 40007 (2011).

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