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Semi-classical approaches to heavy-ion reactions: fusion, rainbow, and glory

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Abstract

A semi-classical approximation has been a powerful tool in understanding the dynamics of low-energy heavy-ion reactions. Here we discuss two topics in this regard, for which Mahir Hussein was a world leading pioneer. The first topic is heavy-ion fusion reactions of neutron-rich nuclei, in which the breakup process of the projectile nucleus plays a crucial role. The second is rainbow and glory scattering, for which characteristic oscillatory patterns in differential cross sections can be well understood in terms of intereferences among several semi-classical trajectories.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The relevant data are all given in the figures.]

References

  1. D.M. Brink, Semi-classical Methods for Nucleus-Nucleus Scattering (Cambridge University Press, Cambridge, England, 1985)

    MATH  Google Scholar 

  2. L.F. Canto, M.S. Hussein, Scattering Theory of Molecules, Atoms and Nuclei (World Scientific Publishing Co Pte. Ltd., Singapore, 2013)

    Book  MATH  Google Scholar 

  3. P. Fröbrich, R. Lipperheide, Theory of Nuclear Reactions (Clarendon Press, Oxford, 1996)

    Google Scholar 

  4. C.H. Dasso, M.I. Gallardo, H.M. Sofia, A. Vitturi, Phys. Rev. C 73, 034612 (2006)

    Article  ADS  Google Scholar 

  5. R.A. Broglia, A. Winther, Heavy Ion Reactions (Westview Press, Cambrigde, 2004)

    Google Scholar 

  6. C. Simenel, Eur. Phys. J. A 48, 152 (2012)

    Article  ADS  Google Scholar 

  7. P. Stevenson, M. Barton, Prog. Part. Nucl. Phys. 104, 142 (2019)

    Article  ADS  Google Scholar 

  8. J. Negele, Rev. Mod. Phys. 54, 913 (1982)

    Article  ADS  Google Scholar 

  9. L.F. Canto, P.R.S. Gomes, R. Donangelo, M.S. Hussein, Phys. Rep. 424, 1 (2006)

    Article  ADS  Google Scholar 

  10. L.F. Canto, P.R.S. Gomes, R. Donangelo, J. Lubian, M.S. Hussein, Phys. Rep. 596, 1 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. M.S. Hussein, M.P. Pato, L.F. Canto, R. Donangelo, Phys. Rev. C 46, 377 (1992)

    Article  ADS  Google Scholar 

  12. M.S. Hussein, K.W. McVoy, Rep. Prog. Part. Nucl. Phys. 12, 103 (1984)

    Article  ADS  Google Scholar 

  13. D.M. Brink, N. Takigawa, Nucl. Phys. A 279, 159 (1977)

    Article  ADS  Google Scholar 

  14. D.T. Khoa, W. von Ortzen, H.G. Bohlen, S. Ohkubo, J. Phys. G Nucl. Part. Phys. 34, R111 (2007)

    Article  Google Scholar 

  15. M. Ueda, M.P. Pato, M.S. Hussein, N. Takigawa, Phys. Rev. Lett. 81, 1809 (1998)

    Article  ADS  Google Scholar 

  16. M. Ueda, M.P. Pato, M.S. Hussein, N. Takigawa, Nucl. Phys. A 648, 229 (1999)

    Article  ADS  Google Scholar 

  17. I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, N. Takahashi, Phys. Rev. Lett. 55, 2676 (1985)

    Article  ADS  Google Scholar 

  18. C. Bachelet, G. Audi, C. Gaulard, C. Guénaut, F. Herfurth, D. Lunney, M. de Saint-Simon, C. Thibault, Phys. Rev. Lett 100, 182501 (2008)

    Article  ADS  Google Scholar 

  19. T. Nakamura, A.M. Vinodkumar, T. Sugimoto, N. Aoi, H. Baba, D. Bazin, N. Fukuda, T. Gomi, H. Hasegawa, N. Imai et al., Phys. Rev. Lett. 96, 252502 (2006)

    Article  ADS  Google Scholar 

  20. C.A. Bertulani, G. Baur, M.S. Hussein, Nucl. Phys. A 526, 751 (1991)

    Article  ADS  Google Scholar 

  21. G.F. Bertsch, H. Esbensen, Ann. Phys. 209, 327 (1991)

    Article  ADS  Google Scholar 

  22. K. Hagino, H. Sagawa, Phys. Rev. C 72, 044321 (2005)

    Article  ADS  Google Scholar 

  23. H. Sagawa, K. Hagino, Eur. Phys. J. A 51, 102 (2015)

    Article  ADS  Google Scholar 

  24. C.A. Bertulani, M.S. Hussein, Phys. Rev. C 76, 051602 (2007)

    Article  ADS  Google Scholar 

  25. K. Hagino, H. Sagawa, Phys. Rev. C 76, 047302 (2007)

    Article  ADS  Google Scholar 

  26. M. Matsuo, K. Mizuyama, Y. Serizawa, Phys. Rev. C 71, 064326 (2005)

    Article  ADS  Google Scholar 

  27. M. Matsuo, Phys. Rev. C 73, 044309 (2006)

    Article  ADS  Google Scholar 

  28. A.B. Balantekin, N. Takigawa, Rev. Mod. Phys. 70, 77 (1998)

    Article  ADS  Google Scholar 

  29. M. Dasgupta, D. Hinde, N. Rowley, A. Stefanini, Ann. Rev. Nucl. Part. Sci. 48, 401 (1998)

    Article  ADS  Google Scholar 

  30. K. Hagino, N. Takigawa, Prog. Theor. Phys. 128, 1061 (2012)

    Article  ADS  Google Scholar 

  31. B.B. Back, H. Esbensen, C.L. Jiang, K.E. Rehm, Rev. Mod. Phys. 86, 317 (2014)

    Article  ADS  Google Scholar 

  32. G. Montagnoli, A.M. Stefanini, Eur. Phys. J. A 53, 169 (2017)

    Article  ADS  Google Scholar 

  33. N. Takigawa, H. Sagawa, Phys. Lett. B 265, 23 (1991)

    Article  ADS  Google Scholar 

  34. H. Sagawa, N. Van Giai, N. Takigawa, M. Ishihara, K. Yasaki, Z. Phys. A 351, 385 (1995)

    Article  ADS  Google Scholar 

  35. C.H. Dasso, A. Vitturi, Phys. Rev. C 50, R12 (1994)

    Article  ADS  Google Scholar 

  36. K. Hagino, A. Vitturi, C.H. Dasso, S.M. Lenzi, Phys. Rev. C 61, 037602 (2000)

    Article  ADS  Google Scholar 

  37. K.S. Choi, M.K. Cheoun, W. So, K. Hagino, K. Kim, Phys. Lett. B 780, 455 (2018)

    Article  ADS  Google Scholar 

  38. M. Ito, K. Yabana, T. Nakatsukasa, M. Ueda, Phys. Lett. B 637, 53 (2006)

    Article  ADS  Google Scholar 

  39. R. Lindsay, N. Rowley, J. Phys. G Nucl. Part. Phys. 10, 805 (1984)

    Article  ADS  Google Scholar 

  40. C.H. Dasso, S. Landowne, A. Winther, Nucl. Phys. A 405, 381 (1983)

    Article  ADS  Google Scholar 

  41. N. Takigawa, M. Kuratani, H. Sagawa, Phys. Rev. C 47, R2470 (1993)

    Article  ADS  Google Scholar 

  42. M.S. Hussein, M.P. Pato, L.F. Canto, R. Donangelo, Phys. Rev. C 47, 2398 (1993)

    Article  ADS  Google Scholar 

  43. Y. Sakuragi, M. Yahiro, M. Kamimura, Prog. Theor. Phys. 70, 1047 (1983)

    Article  ADS  Google Scholar 

  44. Y. Sakuragi, M. Yahiro, M. Kamimura, Prog. Theor. Phys. Suppl. 89, 136 (1986)

    Article  ADS  Google Scholar 

  45. N. Austern, Y. Iseri, M. Kamimura, M. Kawai, G. Rawitscher, M. Yashiro, Phys. Rep. 154, 125 (1987)

    Article  ADS  Google Scholar 

  46. M. Dasgupta, D.J. Hinde, K. Hagino, S.B. Moraes, P.R.S. Gomes, R.M. Anjos, R.D. Butt, A.C. Berriman, N. Carlin, C.R. Morton et al., Phys. Rev. C 66, 041602(R) (2002)

    Article  ADS  Google Scholar 

  47. K. Hagino, M. Dasgupta, D.J. Hinde, Nucl. Phys. A 738, 475 (2004)

    Article  ADS  Google Scholar 

  48. A. Diaz-Torres, D.J. Hinde, J.A. Tostevin, M. Dasgupta, L.R. Gasques, Phys. Rev. Lett. 98, 152701 (2007)

    Article  ADS  Google Scholar 

  49. A. Diaz-Torres, J. Phys. G Nucl. Part. Phys. 37, 075109 (2010)

    Article  ADS  Google Scholar 

  50. D.J. Hinde, M. Dasgupta, B.R. Fulton, C.R. Morton, R.J. Wooliscroft, A.C. Berriman, K. Hagino, Phys. Rev. Lett. 89, 272701 (2002)

    Article  Google Scholar 

  51. A. Diaz-Torres, Comput. Phys. Commun. 182, 1100 (2011)

    Article  ADS  Google Scholar 

  52. A. Diaz-Torres, D. Quraishi, Phys. Rev. C 97, 024611 (2018)

    Article  ADS  Google Scholar 

  53. M. Dasgupta, D.J. Hinde, R.D. Butt, R.M. Anjos, A.C. Berriman, N. Carlin, P.R.S. Gomes, C.R. Morton, J.O. Newton, A. Szanto de Toledo et al., Phys. Rev. Lett. 82, 1395 (1999)

    Article  ADS  Google Scholar 

  54. M. Dasgupta, P.R.S. Gomes, D.J. Hinde, S.B. Moraes, R.M. Anjos, A.C. Berriman, R.D. Butt, N. Carlin, J. Lubian, C.R. Morton et al., Phys. Rev. C 70, 024606 (2004)

    Article  ADS  Google Scholar 

  55. K. Alder, A. Winther, Electromagnetic Excitations (North-Holland, Amsterdam, 1975)

    Google Scholar 

  56. H.D. Marta, L.F. Canto, R. Donangelo, Phys. Rev. C 89, 034625 (2014)

    Article  ADS  Google Scholar 

  57. G.D. Kolinger, L.F. Canto, R. Donangelo, S.R. Souza, Phys. Rev. C 98, 044604 (2018)

    Article  ADS  Google Scholar 

  58. N. Keeley, K.W. Kemper, K. Rusek, Phys. Rev. C 65, 014601 (2001)

    Article  ADS  Google Scholar 

  59. A. Diaz-Torres, I.J. Thompson, C. Beck, Phys. Rev. C 68, 044607 (2003)

    Article  ADS  Google Scholar 

  60. V. Jha, V.V. Parkar, S. Kailas, Phys. Rev. C 89, 034605 (2014)

    Article  ADS  Google Scholar 

  61. P. Descouvemont, T. Druet, L.F. Canto, M.S. Hussein, Phys. Rev. C 91, 024606 (2015)

    Article  ADS  Google Scholar 

  62. A. Diaz-Torres, I.J. Thompson, Phys. Rev. C 65, 024606 (2002)

    Article  ADS  Google Scholar 

  63. J. Rangel, M. Cortes, J. Lubian, L.F. Canto, Phys. Lett. B 803, 135337 (2020)

    Article  Google Scholar 

  64. J. Lei, A.M. Moro, Phys. Rev. Lett. 122, 042503 (2019)

    Article  ADS  Google Scholar 

  65. N. Austern, C.M. Vincent, Phys. Rev. C 23, 1847 (1981)

    Article  ADS  Google Scholar 

  66. M. Ichimura, N. Austern, C.M. Vincent, Phys. Rev. C 32, 431 (1985)

    Article  ADS  Google Scholar 

  67. V.V. Parkar, V. Jha, S. Kailas, Phys. Rev. C 94, 024609 (2016)

    Article  ADS  Google Scholar 

  68. A. Shrivastava, A. Navin, A. Lemasson, K. Ramachandran, V. Nanal, M. Rejmund, K. Hagino, T. Ishikawa, S. Bhattacharyya, A. Chatterjee et al., Phys. Rev. Lett. 103, 232702 (2009)

    Article  ADS  Google Scholar 

  69. A. Shrivastava, A. Navin, A. Diaz-Torres, V. Nanal, K. Ramachandran, M. Rejmund, S. Bhattacharyya, A. Chatterjee, S. Kailas, A. Lemasson et al., Phys. Lett. B 718, 931 (2013)

    Article  ADS  Google Scholar 

  70. S. Hashimoto, K. Ogata, S. Chiba, M. Yahiro, Prog. Theor. Phys. 122, 1291 (2009)

    Article  ADS  Google Scholar 

  71. M. Boselli, A. Diaz-Torres, J. Phys. G Nucl. Part. Phys. 41, 094001 (2014)

    Article  ADS  Google Scholar 

  72. M. Boselli, A. Diaz-Torres, Phys. Rev. C 92, 044610 (2015)

    Article  ADS  Google Scholar 

  73. A. Diaz-Torres, M. Wiescher, Phys. Rev. C 97, 055802 (2018)

    Article  ADS  Google Scholar 

  74. T. Vockerodt, A. Diaz-Torres, Phys. Rev. C 100, 034606 (2019)

    Article  ADS  Google Scholar 

  75. D.A. Goldberg, S.M. Smith, G.F. Burdzik, Phys. Rev. C 10, 1362 (1974)

    Article  ADS  Google Scholar 

  76. M.S. Hussein, H.M. Nussenzveig, A.C.C. Villari, J.L. Cardoso Jr., Phys. Lett. B 114, 1 (1982)

    Article  ADS  Google Scholar 

  77. M.S. Hussein, M.C.B.S. Salvadori, Phys. Lett. B 138, 249 (1984)

    Article  ADS  Google Scholar 

  78. K. Hagino, N. Rowley, EPJ Web Conf. 86, 00014 (2015)

    Article  Google Scholar 

  79. J.B. Ball, C.B. Fulmer, E.E. Gross, D.C. Halbert, M.L. Hensley, C.A. Ludemann, M.J. Saltmars, G.R. Satchler, Nucl. Phys. A 252, 208 (1975)

    Article  ADS  Google Scholar 

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Acknowledgements

This study was funded by Japan Society for the Promotion of Science (Grant number JP19K03861).

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Authors and Affiliations

  1. Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, CP, 68528, Brazil

    L. F. Canto

  2. Department of Physics, Kyoto Unviersity, Kyoto, 606-8502, Japan

    K. Hagino

  3. National Institute of Technology, Akita College, Akita, 011-8511, Japan

    M. Ueda

Authors
  1. L. F. Canto
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  2. K. Hagino
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  3. M. Ueda
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Correspondence to K. Hagino.

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Communicated by Nicolas Alamanos

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Canto, L.F., Hagino, K. & Ueda, M. Semi-classical approaches to heavy-ion reactions: fusion, rainbow, and glory. Eur. Phys. J. A 57, 11 (2021). https://doi.org/10.1140/epja/s10050-020-00312-8

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