Skip to main content

Introduction

  • Chapter
  • First Online:
SU(3) Symmetry in Atomic Nuclei
  • 412 Accesses

Abstract

Elliott’s introduction of SU(3) symmety that generates rotational spectra in quadrupole deformed nuclei from the interacting particle picture, and the appearance of SU(3) in both nuclear shell model and the interacting boson models in many different ways are briefly described. Given also is a short preview of the contents of various chapters in the book.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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. M. Goeppert-Mayer, J.H.D. Jensen, Elementary Theory of Nuclear Shell Structure (Wiley, New York, 1955)

    MATH  Google Scholar 

  2. A. Bohr, B.R. Mottelson, Nuclear Structure Vol II: Nuclear Deformations (W.A. Benjamin, Inc., Reading, 1975)

    Google Scholar 

  3. A. Bohr, B.R. Mottelson, Nuclear Structure, vol. I (W.A.Benjamin Inc., Reading, 1969)

    MATH  Google Scholar 

  4. J.P. Elliott, Collective motion in the nuclear shell model I. Classification schemes for states of mixed configurations. Proc. Roy. Soc. (London) A245, 128–145 (1958)

    Google Scholar 

  5. J.P. Elliott, Collective motion in the nuclear shell model II. The introduction of intrinsic wave-functions. Proc. Roy. Soc. (London) A245, 562–581 (1958)

    Google Scholar 

  6. M. Harvey, The nuclear \(SU(3)\) model. Adv. Nucl. Phys. 1, 67–182 (1968)

    Article  Google Scholar 

  7. J.C. Parikh, Group Symmetries in Nuclear Structure (Plenum, New York, 1978)

    Book  Google Scholar 

  8. P. Vogel, W.E. Ormand, Spin-isospin SU(4) symmetry in sd- and fp-shell nuclei. Phys. Rev. C 47, 623–628 (1993)

    Article  ADS  Google Scholar 

  9. K.T. Hecht, The nuclear shell model in terms of pseudo spin-orbit doublets and pseudo \(SU(3)\) coupling schemes, in Symmetry Properties of Nuclei, Proceedings of the 15th Solvay Conference on Physics, held during September 28–October 3, 1970 (Gordon and Breach, New York, 1974), pp. 301–329

    Google Scholar 

  10. K.T. Hecht, On the origins of pseudo-\(SU(3)\) symmetry, in Nuclear Models, ed. by V.K.B. Kota (Allied Publishers, New Delhi, 2002), pp. 10–19

    Google Scholar 

  11. R.D. Ratnaraju, J.P. Draayer, K.T. Hecht, Search for a coupling scheme in heavy deformed nuclei: the pseudo SU(3) model. Nucl. Phys. A 202, 433–466 (1973)

    Article  ADS  Google Scholar 

  12. K.T. Hecht, A. Adler, Generalized seniority for favored \(J=0\) pairs in mixed configurations. Nucl. Phys. A 137, 129–143 (1969)

    Article  ADS  Google Scholar 

  13. A. Arima, M. Harvey, K. Schimizu, Pseudo \(LS\) coupling and pseudo \(SU_3\) coupling schemes. Phys. Lett. B30, 517–522 (1969)

    Article  ADS  Google Scholar 

  14. J.N. Ginocchio, Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414, 165–261 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  15. V.K.B. Kota, Pseudo-spin to pseudo-\(SU(4)\), in the interacting boson models IBFM, IBFFM and IBM-4, in Nuclear Models, ed. by V.K.B. Kota (Allied Publishers, New Delhi, 2002), pp. 37–48.

    Google Scholar 

  16. J.P. Draayer, K.J. Weeks, Towards a shell model description of the low-energy structure of deformed nuclei I. Even-even systems. Ann. Phys. (N.Y.) 156, 41–67 (1984)

    Google Scholar 

  17. J.P. Draayer, K.J. Weeks, Shell-model description of the low-energy structure of strongly deformed nuclei. Phys. Rev. Lett. 51, 1422–1425 (1983)

    Article  ADS  Google Scholar 

  18. O. Castaños, J.P. Draayer, Y. Leschber, Towards a shell-model description of the low-energy structure of deformed nuclei II. Electromagnetic properties of collective Ml bands. Ann. Phys. (N.Y.) 180, 290–329 (1987)

    Google Scholar 

  19. W. Nazarewicz, P.J. Twin, P. Fallon, J.D. Garrett, Natural-parity states in superdeformed bands and pseudo \(SU(3)\) symmetry at extreme conditions. Phys. Rev. Lett. 64, 1654–1657 (1990)

    Article  ADS  Google Scholar 

  20. F.S. Stephens, M.A. Deleplanque, J.E. Draper, R.M. Diamond, A.O. Macchiavelli, C.W. Beausang, W. Korten, W.H. Kelly, F. Azaiez, J.A. Becker, E.A. Henry, S.W. Yates, M.J. Brinkman, A. Kuhnert, J.A. Cizewski, Pseudo spin symmetry and quantized alignment in nuclei. Phys. Rev. Lett. 65, 301–304 (1990)

    Article  ADS  Google Scholar 

  21. D. Bonatsos, I.E. Assimakis, N. Minkov, A. Martinou, B. Cakirli, R.F. Casten, K. Blaum, Proxy-SU(3) symmetry in heavy deformed nuclei. Phys. Rev. C 95, 064325/1–12 (2017)

    Google Scholar 

  22. D. Bonatsos, I.E. Assimakis, N. Minkov, A. Martinou, S. Sarantopoulou, R.B. Cakirli, R.F. Casten, K. Blaum, Analytic predictions for nuclear shapes, prolate dominance, and the prolate-oblate shape transition in the proxy-SU(3) model. Phys. Rev. C 95, 064326/1–12 (2017)

    Google Scholar 

  23. D. Bonatsos, Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principle. Eur. Phys. J. A53, 148–149 (2017)

    Article  ADS  Google Scholar 

  24. A.P. Zuker, J. Retamosa, A. Poves, E. Caurier, Spherical shell model description of rotational motion. Phys. Rev. C 52, R1741–R1745 (1995)

    Article  ADS  Google Scholar 

  25. G. Martinez-Pinedo, A.P. Zuker, A. Poves, E. Caurier, Full \(pf\) shell study of A=47 and A=49 nuclei. Phys. Rev. C 55, 187–204 (1997)

    Article  ADS  Google Scholar 

  26. A.P. Zuker, A. Poves, F. Nowacki, S.M. Lenzi, Nilsson-\(SU3\) self-consistency in heavy N \(=\) Z nuclei. Phys. Rev. C 92, 024320/1–14 (2015)

    Google Scholar 

  27. G. Rosensteel, D.J. Rowe, Nuclear Sp(3, R) model. Phys. Rev. Lett. 38, 10–14 (1977)

    Article  ADS  Google Scholar 

  28. G. Rosensteel, D.J. Rowe, On the algebraic formulation of collective models III. The sympletic shell model of collective motion. Ann. Phys. (N.Y.) 126, 343–370 (1980)

    Google Scholar 

  29. D.J. Rowe, Microscopic theory of the nuclear collective model. Rep. Prog. Phys. 48, 1419–1480 (1985)

    Article  ADS  Google Scholar 

  30. T. Dytrych, K.D. Launey, J.P. Draayer, P. Maris, J.P. Vary, E. Saule, U. Catalyurek, M. Sosonkina, D. Langr, M.A. Caprio, Collective modes in light nuclei from first principles. Phys. Rev. Lett. 111, 252501/1–5 (2013)

    Google Scholar 

  31. K.D. Launey, J.P. Draayer, T. Dytrych, G.-H. Sun, S.-H. Dong, Approximate symmetries in atomic nuclei from a large-scale shell-model perspective. Int. J. Mod. Phys. E 24, 1530005/1–30 (2015)

    Google Scholar 

  32. K.D. Launey, A.C. Dreyfuss, G.H. Sargsyan, R.B. Baker, M. Miora, J.P. Draayer, T. Dytrych, Ab initio picture of nuclei: shapes, rotations, and vibrations from chiral potentials. Bulg. J. Phys. 44, 345–356 (2017)

    Google Scholar 

  33. A. Arima, F. Iachello, Collective nuclear states as representations of a SU(6) group. Phys. Rev. Lett. 35, 1069–1072 (1975)

    Article  ADS  Google Scholar 

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

    Book  Google Scholar 

  35. D. Janssen, R.V. Jolos, F. Donau, An algebraic treatment of the nuclear quadrupole degree of freedom. Nucl. Phys. A 224, 93–115 (1974)

    Article  ADS  Google Scholar 

  36. R.V. Dzholos, F. Donau, D. Janssen, Symmetry properties of collective states of deformed nuclei. Sov. J. Nucl. Phys. 22, 503–507 (1976)

    Google Scholar 

  37. Y.D. Devi, V.K.B. Kota, sdg interacting boson model: hexadecupole degree of freedom in nuclear structure. Pramana-J. Phys. 39, 413–491 (1992)

    Article  ADS  Google Scholar 

  38. V.K.B. Kota, H. DeMeyer, J. Vander Jeugt, G. Vanden Berghe, Group theoretical aspects of extended interacting boson model. J. Math. Phys. 28, 1644–1652 (1987)

    Google Scholar 

  39. G.L. Long, T.Y. Shen, H.Y. Ji, E.G. Zhao, Analytical expressions for electromagnetic transition rates in the \(SU(3)\) limit of the \(sdpf\) interacting boson model. Phys. Rev. C 57, 2301–2307 (1998)

    Article  ADS  Google Scholar 

  40. H.Y. Ji, G.L. Long, E.G. Zhao, S.W. Xu, Studies of the electric dipole transition of deformed rare-earth nuclei. Nucl. Phys. A 658, 197–216 (1999)

    Article  ADS  Google Scholar 

  41. D. Bohle, A. Richter, W. Steffen, A.E.L. Dieperink, N. Lo Iudice, F. Palumbo, O. Scholten, New magnetic dipole excitation mode studied in the heavy deformed nucleus \(^{156}\)Gd by inelastic electron scattering. Phys. Lett. B137, 27–31 (1984)

    Google Scholar 

  42. V.K.B. Kota, R. Sahu, Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson Model (CRC Press) (Taylor & Francis group, Boca Raton, 2017)

    MATH  Google Scholar 

  43. R. Bijker and V.K.B. Kota, Interacting boson fermion model of collective states: the \(SU(3) \otimes U(2)\) limit. Ann. Phys. (N.Y.) 187, 148–197 (1988)

    Google Scholar 

  44. F. Iachello, P. Van Isacker, The Interacting Boson-Fermion Model (Cambridge University Press, Cambridge, 1991)

    Book  MATH  Google Scholar 

  45. V.K.B. Kota, U.D. Pramanik, Strong coupled and doubly decoupled bands in the \(SU^{BF}(3) \otimes U^F(2j+1)\) limit of interacting boson - fermion - fermion model. Z. Phys. A - Atomic Nuclei 358, 25–31 (1997)

    Google Scholar 

  46. V.K.B. Kota, U.D. Pramanik, \(SU(3)\) coupling schemes for odd-odd nuclei in the interacting boson - fermion - fermion model with both odd proton and odd neutron in natural parity orbits. Eur. Phys. J. A3, 243–253 (1998)

    Google Scholar 

  47. Y.D. Devi, V.K.B. Kota, Correspondence between SU(3) \(\otimes \) U(2) limit of IBF\(^2\)M and two quasi - particle Nilsson configurations. Phys. Lett. B 334, 253–258 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  48. K.T. Hecht, Collective models, in Selected Topics in Nuclear Spectroscopy, ed. by B.J. Verhaar (North Holland, Amsterdam, 1964), pp. 51–105

    Google Scholar 

  49. K.T. Hecht, \(SU_3\) recoupling and fractional parentage in the \(2s-1d\) shell. Nucl. Phys. 62, 1–36 (1965)

    Article  Google Scholar 

  50. J.D. Vergados, \(SU(3) \supset R(3)\) Wigner coefficients in the \(2s-1d\) shell. Nucl. Phys. A 111, 681–754 (1968)

    Article  ADS  Google Scholar 

  51. J.P. Draayer, Y. Akiyama, Wigner and Racah coefficients for \(SU_3\). J. Math. Phys. 14, 1904–1912 (1973)

    Article  ADS  MATH  Google Scholar 

  52. Y. Akiyama, J.P. Draayer, A user’s guide to fortran programs for Wigner and Racah coefficients of \(SU_3\). Comp. Phys. Comm. 5, 405–415 (1973)

    Article  ADS  Google Scholar 

  53. V.K.B. Kota, Plethysm problem of \(U((N+1)(N+2)/2) \supset SU(3)\). J. Phys. A 10, L39–L42 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  54. V.K.B. Kota, Reduction of oscillator orbital symmetry partitions into IR of SU(3), Technical Report PRL-TN-97-78 (Physical Research Laboratory, Ahmedabad, India, 1978)

    Google Scholar 

  55. V.K.B. Kota, Table of reduction of U(10) partitions into SU(3) irreducible components (UMT File of American Mathematical Society). Math. Comput. 39, 302 (1982)

    Article  Google Scholar 

  56. J.P. Draayer, Y. Leschber, S.C. Park, R. Lopez, Representations of \(U(3)\) in \(U(N)\). Comput. Phys. Commun. 56, 279–290 (1989)

    Article  ADS  MATH  Google Scholar 

  57. J.P. Draayer, G. Rosensteel, \(U(3) \rightarrow R(3)\) integrity-basis spectroscopy. Nucl. Phys. A 439, 61–85 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  58. C. Bahri, J.P. Draayer, \(SU(3)\) reduced matrix elements package. Comput. Phys. Commun. 83, 59–94 (1994)

    Article  ADS  MATH  Google Scholar 

  59. O. Castaños, J.P. Draayer, Y. Leschber, Shape variables and the shell model. Z. Phys. A - Atomic Nuclei 329, 33–43 (1988)

    Article  Google Scholar 

  60. B.R. Judd, W. Miller Jr., J. Patera, P. Winternitz, Complete set of commuting operators and \(O(3)\) scalars in the enveloping algebra of \(SU(3)\). J. Math. Phys. 15, 1787–1799 (1974)

    Article  ADS  MATH  Google Scholar 

  61. D.J. Millener, A Note on recoupling coefficients for \(SU(3)\). J. Math. Phys. 19, 1513–1514 (1978)

    Article  ADS  Google Scholar 

  62. V.K.B. Kota, A study of the static moments of odd-odd deformed nuclei. Prog. Theor. Phys. 59, 435–450 (1978)

    Article  ADS  Google Scholar 

  63. V.K.B. Kota, Y.D. Devi, Nuclear Shell Model and the Interacting Boson Model: Lecture Notes for Practitioners (IUC-DAEF Calcutta Center, Kolkata, India, 1996)

    Google Scholar 

  64. K.T. Hecht, D. Braunschweig, Few-nucleon \(SU(3)\) parentage coefficients and \(\alpha \)-particle spectroscopic amplitudes for core excited states in \(s-d\) shell nuclei. Nucl. Phys. A 244, 365–434 (1975)

    Article  ADS  Google Scholar 

  65. K.T. Hecht, Alpha and \(^{8}\)Be cluster amplitudes and core excitations in \(s-d\) shell nuclei. Nucl. Phys. A 283, 223–252 (1977)

    Article  ADS  Google Scholar 

  66. J. Cseh, Algebraic models for shell-like quarteting of nucleons. Phys. Lett. B 743, 213–217 (2015)

    Article  ADS  MATH  Google Scholar 

  67. J. Cseh, G. Riczu, Quartet excitations and cluster spectra in light nuclei. Phys. Lett. B 757, 312–316 (2016)

    Article  ADS  Google Scholar 

  68. A. Leviatan, Partial and quasi dynamical symmetries in quantum many-body systems. J. Phys.: Conf. Ser. 597, 012003/1–17 (2015)

    Google Scholar 

  69. V.K.B. Kota, R. Sahu, P.C. Srivastava, Shell model analysis of multiple \(SU(3)\) algebrs in nuclei. Bulg. J. Phys. 46, 313–324 (2019)

    Google Scholar 

  70. P. Cejnar, J. Jolie, R.F. Casten, Quantum phase transitions in the shapes of atomic nuclei. Rev. Mod. Phys. 82, 2155–2212 (2010)

    Article  ADS  Google Scholar 

  71. V.K.B. Kota, K.B.K. Mayya, J.A. Castilho Alcarás, Statistical law for multiplicities of \(SU(3)\) irreps \((\lambda , \mu )\) in the plethysm \(\{\eta \} \otimes \{m\} \rightarrow (\lambda , \mu )\). J. Phys. A: Math. Theor. 42, 145201/1–20 (2009)

    Google Scholar 

  72. V.K.B. Kota, Two-body ensembles with group symmetries for chaos and regular structures. Int. J. Mod. Phys. E 15, 1869–1883 (2006)

    Article  ADS  Google Scholar 

  73. J.P. Draayer, Fermion models, in Algebraic Approaches to Nuclear Structure: Interacting Boson and Fermion Models, ed. by R.F. Casten (Harwood Academic, Chur, 1993), pp. 423–549

    Google Scholar 

  74. J.G. Hirsch, C.E. Vargas, G. Popa, J.P. Draayer, Pseudo\(+\)Quasi SU(3): towards a shell model description of heavy deformed nuclei, in Computational and Group Theoretical Models in Nuclear Physics, eds. by J. Escher, J.H. Hirsch, S. Pittel, O. Castansos, G. Stoicheva (World Scientific, Singapore, 2004), pp. 31–39

    Google Scholar 

  75. I. Talmi, Simple Models of Complex Nuclei: The Shell Model and the Interacting Boson Model (Harwood, New York, 1993)

    Google Scholar 

  76. P. Van Isacker, Dynamical symmetries in the structure of nuclei. Rep. Prog. Phys. 62, 1661–1717 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  77. A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton, New Jersey, 1974)

    Google Scholar 

  78. A. Frank, P. Van Isacker, Algebraic Methods in Molecular and Nuclear Physics (Wiley, New York, 1994)

    Google Scholar 

  79. J. Lilley, Nuclear Physics: Principles and Applications (Wiley, Singapore, 2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. K. B. Kota .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kota, V.K.B. (2020). Introduction. In: SU(3) Symmetry in Atomic Nuclei. Springer, Singapore. https://doi.org/10.1007/978-981-15-3603-8_1

Download citation

Publish with us

Policies and ethics