1932

Abstract

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by continuous scale invariance, which is broken into discrete scale invariance when three or more particles come into play. This symmetry induces a universal behavior for different systems that is independent of the details of the underlying interaction and rooted in the smallness of the ratio ℓ/ ≪ 1, where the length is associated with the binding energy of the two-body system , and ℓ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the onset of system-specific nonuniversal effects. In this review, we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which → ∞, and we show that nuclear systems belong to this class of universality.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-nucl-102419-032845
2021-09-21
2025-02-16
Loading full text...

Full text loading...

/deliver/fulltext/nucl/71/1/annurev-nucl-102419-032845.html?itemId=/content/journals/10.1146/annurev-nucl-102419-032845&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Chin C, Grimm R, Julienne P, Tiesinga E. Rev. Mod. Phys. 82:1225 2010.
    [Google Scholar]
  2. 2. 
    Luo F, et al. J. Chem. Phys. 98:3564 1993.
    [Google Scholar]
  3. 3. 
    Beane SR, Bedaque PF, Orginos K, Savage MJ. Phys. Rev. Lett. 97:012001 2006.
    [Google Scholar]
  4. 4. 
    Ishii N, Aoki S, Hatsuda T. Phys. Rev. Lett. 99:022001 2007.
    [Google Scholar]
  5. 5. 
    Yamazaki T, Ishikawa K-i, Kuramashi Y, Ukawa A. Phys. Rev. D 92:014501 2015.
    [Google Scholar]
  6. 6. 
    Aoki S, et al. Prog. Theor. Exp. Phys. 2012:1A105 2012.
    [Google Scholar]
  7. 7. 
    Beane S, Detmold W, Orginos K, Savage M. Prog. Part. Nucl. Phys. 66:1 2011.
    [Google Scholar]
  8. 8. 
    Weinberg S. Phys. Lett. B 251:288 1990.
    [Google Scholar]
  9. 9. 
    Weinberg S. Nucl. Phys. B 363:3 1991.
    [Google Scholar]
  10. 10. 
    Ordóñez C, van Kolck U. Phys. Lett. B 291:459 1992.
    [Google Scholar]
  11. 11. 
    Ordóñez C, Ray L, van Kolck U. Phys. Rev. Lett. 72:1982 1994.
    [Google Scholar]
  12. 12. 
    van Kolck U. Phys. Rev. C 49:2932 1994.
    [Google Scholar]
  13. 13. 
    van Kolck U. Prog. Part. Nucl. Phys. 43:337 1999.
    [Google Scholar]
  14. 14. 
    Bedaque PF, van Kolck U. Annu. Rev. Nucl. Part. Sci. 52:339 2002.
    [Google Scholar]
  15. 15. 
    Epelbaum E. Prog. Part. Nucl. Phys. 57:654 2006.
    [Google Scholar]
  16. 16. 
    Epelbaum E, Hammer HW, Meißner UG. Rev. Mod. Phys. 81:1773 2009.
    [Google Scholar]
  17. 17. 
    Machleidt R, Entem DR. Phys. Rep. 503:1 2011.
    [Google Scholar]
  18. 18. 
    Hammer HW, König S, van Kolck U. Rev. Mod. Phys. 92:025004 2020.
    [Google Scholar]
  19. 19. 
    Braaten E, Hammer HW. Phys. Rev. Lett. 91:102002 2003.
    [Google Scholar]
  20. 20. 
    König S, Grießhammer HW, Hammer HW, van Kolck U. Phys. Rev. Lett. 118:202501 2017.
    [Google Scholar]
  21. 21. 
    Gell-Mann M, Oakes RJ, Renner B. Phys. Rev. 175:2195 1968.
    [Google Scholar]
  22. 22. 
    Epelbaum E, Hammer HW, Meißner UG, Nogga A. Eur. Phys. J. C 48:169 2006.
    [Google Scholar]
  23. 23. 
    Beane S, Bedaque P, Savage M, van Kolck U. Nucl. Phys. A 700:377 2002.
    [Google Scholar]
  24. 24. 
    van Kolck U. Nucl. Phys. A 645:273 1999.
    [Google Scholar]
  25. 25. 
    Bedaque P, Hammer HW, van Kolck U. Phys. Rev. Lett. 82:463 1999.
    [Google Scholar]
  26. 26. 
    Bedaque PF, Hammer HW, van Kolck U. Nucl. Phys. A 646:444 1999.
    [Google Scholar]
  27. 27. 
    Kaplan DB, Savage MJ, Wise MB. Phys. Lett. B 424:390 1998.
    [Google Scholar]
  28. 28. 
    Birse MC, McGovern JA, Richardson KG. Phys. Lett. B 464:169 1999.
    [Google Scholar]
  29. 29. 
    Chen JW, Rupak G, Savage MJ. Nucl. Phys. A 653:386 1999.
    [Google Scholar]
  30. 30. 
    Epelbaum E, Gegelia J, Meißner UG. Nucl. Phys. B 925:161 2017.
    [Google Scholar]
  31. 31. 
    Epelbaum E, Gegelia J, Meißner UG. Commun. Theor. Phys. 69:303 2018.
    [Google Scholar]
  32. 32. 
    Grießhammer HW. Nucl. Phys. A 760:110 2005.
    [Google Scholar]
  33. 33. 
    Bethe HA. Phys. Rev. 76:38 1949.
    [Google Scholar]
  34. 34. 
    Efimov V. Phys. Lett. B 33:563 1970.
    [Google Scholar]
  35. 35. 
    Efimov V. Sov. J. Nucl. Phys. 12:589 1971.
    [Google Scholar]
  36. 36. 
    Kraemer T, et al. Nature 440:315 2006.
    [Google Scholar]
  37. 37. 
    Braaten E, Hammer HW. Phys. Rep. 428:259 2006.
    [Google Scholar]
  38. 38. 
    Hammer HW, Platter L. Eur. Phys. J. A 32:113 2007.
    [Google Scholar]
  39. 39. 
    Platter L. Few-Body Syst. 46:139 2009.
    [Google Scholar]
  40. 40. 
    Ferlaino F, Grimm R. Physics 3:9 2010.
    [Google Scholar]
  41. 41. 
    Ferlaino F, et al. Few-Body Syst. 51:113 2011.
    [Google Scholar]
  42. 42. 
    Frederico T, et al. Few-Body Syst. 51:87 2011.
    [Google Scholar]
  43. 43. 
    Greene CH, Giannakeas P, Pérez-Ríos J. Rev. Mod. Phys. 89:035006 2017.
    [Google Scholar]
  44. 44. 
    Naidon P, Endo S. Rep. Prog. Phys. 80:056001 2017.
    [Google Scholar]
  45. 45. 
    Zinner NT, Jensen AS. J. Phys. G 40:053101 2013.
    [Google Scholar]
  46. 46. 
    Marqués FM, et al. Phys. Rev. C 65:044006 2002.
    [Google Scholar]
  47. 47. 
    Kisamori K, et al. Phys. Rev. Lett. 116:052501 2016.
    [Google Scholar]
  48. 48. 
    Deltuva A. Phys. Lett. B 782:238 2018.
    [Google Scholar]
  49. 49. 
    Higgins MD, Greene CH, Kievsky A, Viviani M. Phys. Rev. Lett. 125:052051 2020.
    [Google Scholar]
  50. 50. 
    Yamashita M, Frederico T, Tomio L. Phys. Lett. B 670:49 2008.
    [Google Scholar]
  51. 51. 
    Frederico T, Delfino A, Tomio L, Yamashita M. Prog. Part. Nucl. Phys. 67:939 2012.
    [Google Scholar]
  52. 52. 
    Jensen AS, Riisager K, Fedorov DV, Garrido E. Rev. Mod. Phys. 76:215 2004.
    [Google Scholar]
  53. 53. 
    Hammer HW, Ji C, Phillips DR. J. Phys. G 44:103002 2017.
    [Google Scholar]
  54. 54. 
    Hove D, et al. Phys. Rev. Lett. 120:052502 2018.
    [Google Scholar]
  55. 55. 
    Kievsky A, Marcucci LE, Rosati S, Viviani M. Few-Body Syst. 22:1 1997.
    [Google Scholar]
  56. 56. 
    Kievsky A, et al. J. Phys. G 35:063101 2008.
    [Google Scholar]
  57. 57. 
    Gattobigio M, Kievsky A, Viviani M, Barletta P. Phys. Rev. A 79:032513 2009.
    [Google Scholar]
  58. 58. 
    Gattobigio M, Kievsky A, Viviani M, Barletta P. Few-Body Syst. 45:127 2009.
    [Google Scholar]
  59. 59. 
    Varga K, Suzuki Y. Phys. Rev. C 52:2885 1995.
    [Google Scholar]
  60. 60. 
    Bargmann V. Rev. Mod. Phys. 21:488 1949.
    [Google Scholar]
  61. 61. 
    Babenko V, Petrov N. Phys. At. Nucl. 71:50 2008.
    [Google Scholar]
  62. 62. 
    Aziz RA, Slaman MJ. J. Chem. Phys. 94:8047 1991.
    [Google Scholar]
  63. 63. 
    Wiringa RB, Stoks VGJ, Schiavilla R. Phys. Rev. C 51:38 1995.
    [Google Scholar]
  64. 64. 
    Grisenti R, et al. Phys. Rev. Lett. 85:2284 2000.
    [Google Scholar]
  65. 65. 
    Zaccanti M, et al. Nat. Phys. 5:586 2009.
    [Google Scholar]
  66. 66. 
    Berninger M, et al. Phys. Rev. Lett. 107:120401 2011.
    [Google Scholar]
  67. 67. 
    Machtey O, Shotan Z, Gross N, Khaykovich L. Phys. Rev. Lett. 108:210406 2012.
    [Google Scholar]
  68. 68. 
    Roy S, et al. Phys. Rev. Lett. 111:053202 2013.
    [Google Scholar]
  69. 69. 
    Klauss CE, et al. Phys. Rev. Lett. 119:143401 2017.
    [Google Scholar]
  70. 70. 
    Thomas LH. Phys. Rev. 47:903 1935.
    [Google Scholar]
  71. 71. 
    Gattobigio M, Göbel M, Hammer HW, Kievsky A. Few-Body Syst. 60:40 2019.
    [Google Scholar]
  72. 72. 
    Álvarez-Rodríguez R, Deltuva A, Gattobigio M, Kievsky A. Phys. Rev. A 93:062701 2016.
    [Google Scholar]
  73. 73. 
    Kharchenko VF. Sov. J. Nucl. Phys. 16:173 1972.
    [Google Scholar]
  74. 74. 
    Kievsky A, Gattobigio M. Phys. Rev. A 87:052719 2013.
    [Google Scholar]
  75. 75. 
    Kievsky A, Timofeyuk NK, Gattobigio M. Phys. Rev. A 90:032504 2014.
    [Google Scholar]
  76. 76. 
    Gattobigio M, Kievsky A. Phys. Rev. A 90:012502 2014.
    [Google Scholar]
  77. 77. 
    Kievsky A, Gattobigio M. Phys. Rev. A 92:062715 2015.
    [Google Scholar]
  78. 78. 
    Gogolin AO. Phys. Rev. Lett. 100:140404 2008.
    [Google Scholar]
  79. 79. 
    Deltuva A, Gattobigio M, Kievsky A, Viviani M. Phys. Rev. C 102:064001 2020.
    [Google Scholar]
  80. 80. 
    Hiyama E, Kamimura M. Phys. Rev. A 90:052514 2014.
    [Google Scholar]
  81. 81. 
    Kievsky A, et al. Phys. Rev. A 102:063320 2020.
    [Google Scholar]
  82. 82. 
    Efimov V. Sov. J. Nucl. Phys. 29:546 1979.
    [Google Scholar]
  83. 83. 
    Carbonell J, Deltuva A, Lazauskas R. Comp. Rend. Phys. 12:47 2011.
    [Google Scholar]
  84. 84. 
    Deltuva A. Phys. Rev. C 102:034003 2020.
    [Google Scholar]
  85. 85. 
    Kievsky A, Gattobigio M. Few-Body Syst. 57:217 2016.
    [Google Scholar]
  86. 86. 
    Gattobigio M, Kievsky A, Viviani M. Phys. Rev. C 100:034004 2019.
    [Google Scholar]
  87. 87. 
    Phillips AC. Rep. Prog. Phys. 40:905 1977.
    [Google Scholar]
  88. 88. 
    Rakityansky SA, Sofianos SA, Elander N. J. Phys. A 40:14857 2007.
    [Google Scholar]
  89. 89. 
    Girard BA, Fuda MG. Phys. Rev. C 19:579 1979.
    [Google Scholar]
  90. 90. 
    Orlov YV, Nikitina LI. Phys. At. Nucl. 69:607 2006.
    [Google Scholar]
  91. 91. 
    Adhikari SK, Fonseca AC, Tomio L. Phys. Rev. C 27:1826 1983.
    [Google Scholar]
  92. 92. 
    Rupak G, Vaghani A, Higa R, van Kolck U. Phys. Lett. B 791:414 2019.
    [Google Scholar]
  93. 93. 
    Lewerenz M. J. Chem. Phys. 106:4596 1997.
    [Google Scholar]
  94. 94. 
    Deltuva A. Phys. Rev. A 82:040701(R) 2010.
    [Google Scholar]
  95. 95. 
    Gattobigio M, Kievsky A, Viviani M. Phys. Rev. A 84:052503 2011.
    [Google Scholar]
  96. 96. 
    Gattobigio M, Kievsky A, Viviani M. Phys. Rev. A 86:042513 2012.
    [Google Scholar]
  97. 97. 
    Deltuva A. Phys. Rev. A 85:042705 2012.
    [Google Scholar]
  98. 98. 
    Deltuva A. Few-Body Syst. 54:569 2013.
    [Google Scholar]
  99. 99. 
    Greene CH. Phys. Today 63:40 2010.
    [Google Scholar]
  100. 100. 
    Kievsky A, Gattobigio M, Timofeyuk NK. Few-Body Syst. 55:945 2014.
    [Google Scholar]
  101. 101. 
    Bazak B, Eliyahu M, van Kolck U. Phys. Rev. A 94:052502 2016.
    [Google Scholar]
  102. 102. 
    D'Incao J, von Stecher J, Greene C. Phys. Rev. Lett. 103:033004 2009.
    [Google Scholar]
  103. 103. 
    von Stecher J, D'Incao JP, Greene CH. Nat. Phys. 5:417 2009.
    [Google Scholar]
  104. 104. 
    von Stecher J. J. Phys. B 43:101002 2010.
    [Google Scholar]
  105. 105. 
    Pandharipande VR, et al. Phys. Rev. Lett. 50:1676 1983.
    [Google Scholar]
  106. 106. 
    Aziz RA, et al. J. Chem. Phys. 70:4330 1979.
    [Google Scholar]
  107. 107. 
    Kievsky A, Polls A, Juliá-Díaz B, Timofeyuk NK. Phys. Rev. A 96:040501(R) 2017.
    [Google Scholar]
  108. 108. 
    van Kolck U. Few-Body Syst. 58:112 2017.
    [Google Scholar]
  109. 109. 
    Tan S. Ann. Phys. 323:2952 2008.
    [Google Scholar]
  110. 110. 
    Tan S. Ann. Phys. 323:2971 2008.
    [Google Scholar]
  111. 111. 
    Weiss R, Bazak B, Barnea N. Phys. Rev. Lett. 114:012501 2015.
    [Google Scholar]
  112. 112. 
    Weiss R, Pazy E, Barnea N. Few-Body Syst. 58:9 2017.
    [Google Scholar]
  113. 113. 
    Garrido E, Gattobigio M, Kievsky A. Phys. Rev. A 88:032701 2013.
    [Google Scholar]
  114. 114. 
    Ji C, Braaten E, Phillips DR, Platter L. Phys. Rev. A 92:030702(R) 2015.
    [Google Scholar]
  115. 115. 
    Platter L, Hammer HW, Meißner UG. Phys. Lett. B 607:254 2005.
    [Google Scholar]
  116. 116. 
    Gattobigio M, Kievsky A, Viviani M. Phys. Rev. C 83:024001 2011.
    [Google Scholar]
  117. 117. 
    Hammer HW. Few-Body Syst. 59:58 2018.
    [Google Scholar]
  118. 118. 
    Pudliner BS, Pandharipande VR, Carlson J, Wiringa RB. Phys. Rev. Lett. 74:4396 1995.
    [Google Scholar]
  119. 119. 
    Kievsky A, Viviani M, Gattobigio M, Girlanda L. Phys. Rev. C 95:024001 2017.
    [Google Scholar]
  120. 120. 
    Lepage GP How to renormalize the Schrödinger equation. Nuclear Physics: Proceedings of the VIII Jorge André Swieca Summer School, 1995 CA Bertulani et al.135–80 Singapore: World Sci 1997.
    [Google Scholar]
  121. 121. 
    Lepage GP The analysis of algorithms for lattice field theory. From Actions to Answers: Proceedings of the 1989 Theoretical Advanced Study Institute in Elementary Particle Physics TA DeGrand, D Toussaint 97–120 Singapore: World Sci 1989.
    [Google Scholar]
  122. 122. 
    Entem DR, Machleidt R. Phys. Rev. C 68:041001 2003.
    [Google Scholar]
  123. 123. 
    Entem DR, Machleidt R, Nosyk Y. Phys. Rev. C 96:024004 2017.
    [Google Scholar]
  124. 124. 
    Epelbaum E, Krebs H, Meißner UG. Phys. Rev. Lett. 115:122301 2015.
    [Google Scholar]
  125. 125. 
    Epelbaum E, Meißner UG, Glöckle W. Nucl. Phys. A 714:535 2003.
    [Google Scholar]
  126. 126. 
    Gattobigio M, Kievsky A, Viviani M. Few-Body Syst. 54:657 2013.
    [Google Scholar]
  127. 127. 
    Kievsky A, et al. Phys. Rev. Lett. 121:072701 2018.
    [Google Scholar]
  128. 128. 
    Bombaci I, Logoteta D. Astron. Astrophys. 609:A128 2018.
    [Google Scholar]
  129. 129. 
    Logoteta D, Bombaci I, Kievsky A. Phys. Rev. C 94:064001 2016.
    [Google Scholar]
  130. 130. 
    Logoteta D, Bombaci I, Kievsky A. Phys. Lett. B 758:449 2016.
    [Google Scholar]
  131. 131. 
    Babenko VA, Petrov NM. Phys. At. Nucl. 63:1709 2000.
    [Google Scholar]
  132. 132. 
    Newton RG. Scattering Theory of Waves and Particles Berlin/Heidelberg, Ger: Springer 1982.
    [Google Scholar]
  133. 133. 
    Girlanda L, Kievsky A, Viviani M, Marcucci LE. Phys. Rev. C 99:054003 2019.
    [Google Scholar]
  134. 134. 
    Girlanda L, Kievsky A, Marcucci LE, Viviani M. Phys. Rev. C 102:034007 2020.
    [Google Scholar]
/content/journals/10.1146/annurev-nucl-102419-032845
Loading
/content/journals/10.1146/annurev-nucl-102419-032845
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error