Skip to main content
SpringerLink
Log in

Symmetry in Nuclear Physics: The Interacting Boson Model

  • Chapter
  • First Online:
Symmetries in Atomic Nuclei

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 230))

  • 618 Accesses

Abstract

In the second group of symmetry-based models, a nucleus is treated as a system of interacting bosons which are of composite character and represent correlated pairs of nucleons. The choice of the different bosons is dictated by the nature of the nucleonic interactions and also depends on the particular nucleus that is considered, as is discussed in Sect. 3.1. Throughout this chapter we pay particular attention to the connections that can be established via symmetry techniques between the nuclear shell model and the interacting boson model. We close the chapter with a detailed study of the nucleus112Cd in Sect. 3.6 which illustrates how such symmetries are studied experimentally.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. National Nuclear Data Center: http://www.nndc.bnl.gov

  2. A. Bohr, B.R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, No 16 (1953)

    Google Scholar 

  3. A. Bohr, B.R. Mottelson, Nuclear Structure. II Nuclear Deformations (Benjamin, New York, 1975)

    Google Scholar 

  4. N.V. Zamfir, R.F. Casten, D.S. Brenner, Phys. Rev. Lett. 72, 3480 (1994)

    Article  ADS  Google Scholar 

  5. A. Arima, F. Iachello, Phys. Rev. Lett. 35, 1069 (1975)

    Article  ADS  Google Scholar 

  6. F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, 1987)

    Book  Google Scholar 

  7. T. Otsuka, A. Arima, F. Iachello, Nucl. Phys. A 309, 1 (1978)

    Article  ADS  Google Scholar 

  8. O. Castaños, E. Chacón, A. Frank, M. Moshinsky, J. Math. Phys. 20, 35 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Arima, F. Iachello, Ann. Phys. (NY) 99, 253 (1976)

    Article  ADS  Google Scholar 

  10. A. Arima, F. Iachello, Ann. Phys. (NY) 111, 201 (1978)

    Article  ADS  Google Scholar 

  11. A. Arima, F. Iachello, Ann. Phys. (NY) 123, 468 (1979)

    Article  ADS  Google Scholar 

  12. A. Arima, F. Iachello, Phys. Rev. Lett. 40, 385 (1978)

    Article  ADS  Google Scholar 

  13. J.A. Cizewski, R.F. Casten, G.J. Smith, M.L. Stelts, W.R. Kane, H.G. Börner, W.F. Davidson, Phys. Rev. Lett. 40, 167 (1978)

    Article  ADS  Google Scholar 

  14. R.F. Casten, J.A. Cizewski, Phys. Lett. B 79, 5 (1978)

    Article  ADS  Google Scholar 

  15. R.F. Casten, in Interacting Bose–Fermi Systems in Nuclei, ed. by F. Iachello (Plenum, New York, 1981), p. 3

    Chapter  Google Scholar 

  16. A. Leviatan, A. Novoselsky, I. Talmi, Phys. Lett. B 172, 144 (1986)

    Article  ADS  Google Scholar 

  17. J. Jolie, H. Lehmann, Phys. Lett. B 342, 1 (1995)

    Article  ADS  Google Scholar 

  18. D.D. Warner, R.F. Casten, Phys. Rev. Lett. 48, 1385 (1982)

    Article  ADS  Google Scholar 

  19. H.G. Börner, J. Jolie, S. Robinson, R.F. Casten, J.A. Cizewski, Phys. Rev. C 42, R2271 (1990)

    Article  ADS  Google Scholar 

  20. J. Jolie et al., Nucl. Phys. A 934, 1 (2015)

    Article  ADS  Google Scholar 

  21. C.S. Lim, R.H. Spear, M.P. Fewell, G.J. Gyapong, Nucl. Phys. A 548, 308 (1992)

    Article  ADS  Google Scholar 

  22. J. Jolie, A. Linnemann, Phys. Rev. C 68, 031301(R) (2003)

    Google Scholar 

  23. A.M. Shirokov, N.A. Smirnova, Yu.F. Smirnov, Phys. Lett. B 434, 237 (1998)

    Article  ADS  Google Scholar 

  24. D. Kusnezov, Phys. Rev. Lett. 79, 537 (1997)

    Article  ADS  Google Scholar 

  25. P. Cejnar, J. Jolie, Phys. Lett. B 420, 241 (1998)

    Article  ADS  Google Scholar 

  26. F. Pan, J.P. Draayer, Nucl. Phys. A 636, 156 (1998)

    Article  ADS  Google Scholar 

  27. O. Scholten, F. Iachello, A. Arima, Ann. Phys. (NY) 115, 325 (1978)

    Article  ADS  Google Scholar 

  28. R.F. Casten, J.A. Cizewski, Nucl. Phys. A 309, 477 (1978)

    Article  ADS  Google Scholar 

  29. J. Stachel, P. Van Isacker, K. Heyde, Phys. Rev. C 25, 650 (1982)

    Article  ADS  Google Scholar 

  30. D. Bonatsos, Interacting Boson Models of Nuclear Structure (Clarendon, Oxford, 1988)

    MATH  Google Scholar 

  31. Y.D. Devi, V.K.B. Kota, Pramana J. Phys. 39, 413 (1992)

    Article  ADS  Google Scholar 

  32. J. Engel, F. Iachello, Phys. Rev. Lett. 54, 1126 (1985)

    Article  ADS  Google Scholar 

  33. J.N. Ginocchio, M.W. Kirson, Phys. Rev. Lett. 44, 1744 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  34. A. Bohr, B.R. Mottelson, Phys. Scr. 22, 468 (1980)

    Article  ADS  Google Scholar 

  35. D.M. Brink, A.F.R. De Toledo Piza, A.K. Kerman, Phys. Lett. 19, 413 (1965)

    Article  ADS  Google Scholar 

  36. L. Wilets, M. Jean, Phys. Rev. C 102, 788 (1956)

    Article  ADS  Google Scholar 

  37. J.P. Elliott, J.A. Evans, P. Park, Phys. Lett. B 169, 309 (1986)

    Article  ADS  Google Scholar 

  38. R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley, New York, 1981)

    MATH  Google Scholar 

  39. E. López-Moreno, O. Castaños, Phys. Rev. C 54, 2374 (1996)

    Article  ADS  Google Scholar 

  40. J. Jolie, R.F. Casten, P. von Brentano, V. Werner, Phys. Rev. Lett. 87, 162501 (2001)

    Article  ADS  Google Scholar 

  41. D.D. Warner, R.F. Casten, Phys. Rev. C 28, 1798 (1983)

    Article  ADS  Google Scholar 

  42. P.O. Lipas, P. Toivonen, D.D. Warner, Phys. Lett. B 155, 295 (1985)

    Article  ADS  Google Scholar 

  43. F. Iachello, N.V. Zamfir, R.F. Casten, Phys. Rev. Lett. 81, 1191 (1998)

    Article  ADS  Google Scholar 

  44. J. Jolie, P. Cejnar, R.F. Casten, S. Heinze, A. Linnemann, V. Werner, Phys. Rev. Lett. 89, 182502 (2002)

    Article  ADS  Google Scholar 

  45. P. Cejnar, S. Heinze, J. Jolie, Phys. Rev. C 68, 034326 (2003)

    Article  ADS  Google Scholar 

  46. L. Landau, Phys. Z. Sowjet. 11, 26 & 545 (1937); reprinted in Collected Papers of L.D. Landau (Pergamon, Oxford, 1965), p. 193

    Google Scholar 

  47. R.F. Casten, Nature Phys. 2, 811 (2006)

    Article  ADS  Google Scholar 

  48. P. Cejnar, J. Jolie, Phys. Rev. E 61, 6237 (2000)

    Article  ADS  Google Scholar 

  49. V. Werner, P. von Brentano, R.F. Casten, J. Jolie, Phys. Lett. B 527, 55 (2002)

    Article  ADS  Google Scholar 

  50. R.F. Casten, Prog. Part. Nucl. Phys. 62, 183 (2009)

    Article  ADS  Google Scholar 

  51. P. Cejnar, J. Jolie, R.F. Casten, Rev. Mod. Phys. 82, 2155 (2010)

    Article  ADS  Google Scholar 

  52. Y. Alhassid, A. Leviatan, J. Phys. A: Math. Gen. 25, L1265 (1992)

    Article  ADS  Google Scholar 

  53. A. Leviatan, Phys. Rev. Lett. 77, 818 (1996)

    Article  ADS  Google Scholar 

  54. P. Van Isacker, Phys. Rev. Lett. 83, 4269 (1999)

    Article  ADS  Google Scholar 

  55. A. Leviatan, P. Van Isacker, Phys. Rev. Lett. 89, 222501 (2002)

    Article  ADS  Google Scholar 

  56. A. Leviatan, J.E. García–Ramos, P. Van Isacker, Phys. Rev. C 87, 021302(R) (2013)

    Google Scholar 

  57. J.E. García-Ramos, A. Leviatan, P. Van Isacker, Phys. Rev. Lett. 102, 112502 (2009)

    Article  ADS  Google Scholar 

  58. E. Tavukcu et al., Phys. Rev. C 65, 064309 (2002)

    Article  ADS  Google Scholar 

  59. R.F. Casten, P. von Brentano, K. Heyde, P. Van Isacker, J. Jolie, Nucl. Phys. A 439, 289 (1985)

    Article  ADS  Google Scholar 

  60. P. Van Isacker, Nucl. Phys. News 24(3), 23 (2014)

    Article  Google Scholar 

  61. C. Kremer, J. Beller, A. Leviatan, N. Pietralla, G. Rainovski, R. Trippel, P. Van Isacker, Phys. Rev. C 89, 041302(R) (2014)

    Google Scholar 

  62. D.J. Rowe, P. Rochford, J. Repka, J. Math. Phys. 29, 572 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  63. D.J. Rowe, C. Bahri, W. Wijesundera, Phys. Rev. Lett. 80, 4394 (1998)

    Article  ADS  Google Scholar 

  64. D. Bonatsos, E.A. McCutchan, R.F. Casten, Phys. Rev. Lett. 104, 022502 (2010)

    Article  ADS  Google Scholar 

  65. J.L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, P. Van Duppen, Phys. Rep. 215, 101 (1992)

    Article  ADS  Google Scholar 

  66. A. Bäcklin, N.G. Jonsson, R. Julin, J. Kantele, M. Luontama, A. Passoja, T. Poikolainen, Nucl. Phys. A 351, 490 (1981)

    Article  ADS  Google Scholar 

  67. P.D. Duval, B.R. Barrett, Phys. Lett. B 100, 223 (1981)

    Article  ADS  Google Scholar 

  68. K. Heyde, C. De Coster, J. Jolie, J.L. Wood, Phys. Rev. C 46, 541 (1992)

    Article  ADS  Google Scholar 

  69. G. Scharff-Goldhaber, J. Wesener, Phys. Rev. 98, 212 (1955)

    Article  ADS  Google Scholar 

  70. B.L. Cohen, R.E. Price, Phys. Rev. 121, 1441 (1961)

    Article  ADS  Google Scholar 

  71. D.R. Bès, G.G. Dussel, Nucl. Phys. A 135, 1 (1969)

    Article  ADS  Google Scholar 

  72. H.W. Fielding et al., Nucl. Phys. A 281, 389 (1977)

    Article  ADS  Google Scholar 

  73. J. Kumpulainen et al., Phys. Rev. C 45, 640 (1992)

    Article  ADS  Google Scholar 

  74. K. Heyde et al., Nucl. Phys. A 466, 189 (1987)

    Article  ADS  Google Scholar 

  75. P.J. Twin et al., Phys. Rev. Lett. 57, 811 (1986)

    Article  ADS  Google Scholar 

  76. D. Darquennes et al., Phys. Rev. C 42, R804 (1990)

    Article  ADS  Google Scholar 

  77. M. Délèze, S. Drissi, J. Jolie, J. Kern, J.P. Vorlet, Nucl. Phys. A 554, 1 (1993)

    Article  ADS  Google Scholar 

  78. M. Délèze, S. Drissi, J. Kern, P.A. Tercier, J.P. Vorlet, J. Rikovska, T. Otsuka, S. Judge, A. Williams, Nucl. Phys. A 551, 269 (1993)

    Article  ADS  Google Scholar 

  79. J. Kern, Phys. Lett. B 320, 7 (1994)

    Article  ADS  Google Scholar 

  80. D. Kusnezov, OCTUPOLE. Computer Code (Yale University, New Haven, 1987)

    Google Scholar 

  81. R. Hertenberger et al., Nucl. Phys. A 574, 414 (1994)

    Article  ADS  Google Scholar 

  82. T. Belgya, G. Molnár, S.W. Yates, Nucl. Phys. A 607, 43 (1996)

    Article  ADS  Google Scholar 

  83. P.E. Garrett, H. Lehmann, C.A. McGrath, M. Yeh, S.W. Yates, Phys. Rev. C 54, 2259 (1996)

    Article  ADS  Google Scholar 

  84. H. Lehmann, J. Jolie, C. De Coster, B. Decroix, K. Heyde, J.L. Wood, Nucl. Phys. A 621, 767 (1997)

    Article  ADS  Google Scholar 

  85. C. De Coster, K. Heyde, B. Decroix, P. Van Isacker, J. Jolie, H. Lehmann, J.L. Wood, Nucl. Phys. A 600, 251 (1996)

    Article  ADS  Google Scholar 

  86. P.E. Garrett, H. Lehmann, J. Jolie, C.A. McGrath, M. Yeh, S.W. Yates, Phys. Rev. C 59, 2455 (1999)

    Article  ADS  Google Scholar 

  87. D.S. Jamieson et al., Phys. Rev. C 90, 054312 (2014)

    Article  ADS  Google Scholar 

  88. P.E. Garrett, H. Lehmann, J. Jolie, C.A. McGrath, M. Yeh, W. Younes, S.W. Yates, Phys. Rev. C 64, 024316 (2001)

    Article  ADS  Google Scholar 

  89. P.E. Garrett, K.L. Green, H. Lehmann, J. Jolie, C.A. McGrath, M. Yeh, S.W. Yates, Phys. Rev. C 75, 054310 (2007)

    Article  ADS  Google Scholar 

  90. A. Leviatan, N. Gavrielov, J.E. García-Ramos, P. Van Isacker, Phys. Rev. C 98, 031302(R) (2018)

    Google Scholar 

  91. D. Bandyopadhyay et al., Phys. Rev. C 68, 014324 (2003)

    Article  ADS  Google Scholar 

  92. P.E. Garrett et al., Phys. Rev. C 86, 044304 (2012)

    Article  ADS  Google Scholar 

  93. A.E.L. Dieperink, O. Scholten, F. Iachello, Phys. Rev. Lett. 44, 1747 (1980)

    Article  ADS  Google Scholar 

  94. P. Cejnar, J. Jolie, Prog. Part. Nucl. Phys. 62, 210 (2009)

    Article  ADS  Google Scholar 

  95. C. Bahri, D.J. Rowe, Nucl. Phys. A 662, 125 (2000)

    Article  ADS  Google Scholar 

  96. M. Macek, J. Dobeš, P. Cejnar, Phys. Rev. C 80, 014319 (2009)

    Article  ADS  Google Scholar 

  97. M. Kadi et al., Phys. Rev. C 68, 031306(R) (2003)

    Google Scholar 

  98. J.C. Batchelder et al., Phys. Rev. C 80, 054318 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Sciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, México D.F., Mexico

    Alejandro Frank

  2. Universität zu Köln, Institut für Kernphysik, Köln, Germany

    Jan Jolie

  3. Grand Accélérateur National d’Ions Lourds (GANIL), Caen, France

    Pieter Van Isacker

Authors
  1. Alejandro Frank
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Jolie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pieter Van Isacker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Frank, A., Jolie, J., Isacker, P.V. (2019). Symmetry in Nuclear Physics: The Interacting Boson Model. In: Symmetries in Atomic Nuclei. Springer Tracts in Modern Physics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-030-21931-4_3

Download citation

Publish with us

Policies and ethics

Search

Navigation