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Symmetries of the interacting boson model

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Abstract

This contribution reviews the symmetry properties of the interacting boson model of Arima and Iachello. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of partial dynamical symmetry and quasi dynamical symmetry, which can be beautifully illustrated in the context of the interacting boson model. The main conclusion of the analysis is that dynamical symmetries are scarce while their partial and quasi extensions are ubiquitous.

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References

  1. A. Arima and F. Iachello, Collective nuclear states as representations of a SU(6) group, Phys. Rev. Lett. 35(16), 1069 (1975)

    ADS  Google Scholar 

  2. J. Rainwater, Nuclear energy level argument for a spheroidal nuclear model, Phys. Rev. 79(3), 432 (1950)

    ADS  MATH  Google Scholar 

  3. A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 26, 14 (1952)

    Google Scholar 

  4. D. M. Brink, A. F. R. De Toledo Piza, and A. K. Kerman, Interval rules and intensity ratios in vibrating spherical nuclei, Phys. Lett. 19(5), 413 (1965)

    ADS  Google Scholar 

  5. A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, 16 (1953)

    Google Scholar 

  6. L. Wilets and M. Jean, Surface oscillations in even-even nuclei, Phys. Rev. C 102, 788 (1956)

    ADS  MATH  Google Scholar 

  7. A. Arima, T. Otsuka, F. Iachello, and I. Talmi, Collective nuclear states as symmetric couplings of proton and neutron excitations, Phys. Lett. B 66(3), 205 (1977)

    ADS  Google Scholar 

  8. T. Otsuka, A. Arima, and F. Iachello, Nuclear shell model and interacting bosons, Nucl. Phys. A 309(1–2), 1 (1978)

    ADS  Google Scholar 

  9. T. Otsuka, A. Arima, F. Iachello, and I. Talmi, Shell model description of interacting bosons, Phys. Lett. B 76(2), 139 (1978)

    ADS  Google Scholar 

  10. J. P. Elliott and A. P. White, An isospin invariant form of the interacting boson model, Phys. Lett. B 97(2), 169 (1980)

    ADS  Google Scholar 

  11. J. P. Elliott and J. A. Evans, An intrinsic spin for interacting bosons, Phys. Lett. B 101(4), 216 (1981)

    ADS  Google Scholar 

  12. E. Wigner, On the consequences of the symmetry of the nuclear hamiltonian on the spectroscopy of nuclei, Phys. Rev. 51(2), 106 (1937)

    ADS  MATH  Google Scholar 

  13. G. Racah, Theory of complex spectra (III), Phys. Rev. 63(9–10), 367 (1943)

    ADS  Google Scholar 

  14. G. Racah, Theory of complex spectra (IV), Phys. Rev. 76(9), 1352 (1949)

    ADS  MATH  Google Scholar 

  15. J. P. Elliott, Collective motion in the nuclear shell model (I): Classification schemes for states of mixed configurations, Proc. R. Soc. Lond. A 245(1240), 128 (1958)

    ADS  MathSciNet  MATH  Google Scholar 

  16. J. P. Elliott, Collective motion in the nuclear shell model (II): The introduction of intrinsic wave-functions, Proc. R. Soc. Lond. A 245(1243), 562 (1958)

    ADS  MathSciNet  MATH  Google Scholar 

  17. F. Iachello, Lie Algebras and Applications, Springer, Berlin, 2006

    MATH  Google Scholar 

  18. A. Frank, J. Jolie, and P. Van Isacker, Symmetries in Atomic Nuclei, Springer, Berlin, 2009

    MATH  Google Scholar 

  19. P. Van Isacker, Partial and quasi dynamical symmetries in nuclei, Nucl. Phys. News 24(3), 23 (2014)

    Google Scholar 

  20. J. N. Ginocchio and M. W. Kirson, Relationship between the Bohr collective hamiltonian and the interacting-boson model, Phys. Rev. Lett. 44(26), 1744 (1980)

    ADS  MathSciNet  MATH  Google Scholar 

  21. A. E. L. Dieperink, O. Scholten, and F. Iachello, Classical limit of the interacting-boson model, Phys. Rev. Lett. 44(26), 1747 (1980)

    ADS  Google Scholar 

  22. A. Bohr and B. R. Mottelson, Features of nuclear deformations produced by the alignment of individual particles or pairs, Phys. Scr. 22(5), 468 (1980)

    ADS  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  24. R. Gilmore, Catastrophe Theory for Scientists and Engineers, Wiley, New York, 1981

    MATH  Google Scholar 

  25. E. López-Moreno and O. Castaños, Shapes and stability within the interacting boson model: Dynamical symmetries, Phys. Rev. C 54(5), 2374 (1996)

    ADS  Google Scholar 

  26. J. Jolie, P. Cejnar, R. F. Casten, S. Heinze, A. Linnemann, and V. Werner, Triple point of nuclear deformations, Phys. Rev. Lett. 89(18), 182502 (2002)

    ADS  Google Scholar 

  27. R. F. Casten, Shape phase transitions and critical-point phenomena in atomic nuclei, Nat. Phys. 2(12), 811 (2006)

    Google Scholar 

  28. P. Cejnar, J. Jolie, and R. F. Casten, Quantum phase transitions in the shapes of atomic nuclei, Rev. Mod. Phys. 82(3), 2155 (2010)

    ADS  Google Scholar 

  29. O. Castaños, E. Chacón, A. Frank, and M. Moshinsky, Group theory of the interacting boson model of the nucleus, J. Math. Phys. 20(1), 35 (1979)

    ADS  MathSciNet  MATH  Google Scholar 

  30. A. Arima and F. Iachello, Interacting boson model of collective states (I): The vibrational limit, Ann. Phys. 99(2), 253 (1976)

    ADS  Google Scholar 

  31. A. Arima and F. Iachello, Interacting boson model of collective nuclear states (II): The rotational limit, Ann. Phys. 111(1), 201 (1978)

    ADS  Google Scholar 

  32. A. Arima and F. Iachello, Interacting boson model of collective nuclear states (IV): The O(6) limit, Ann. Phys. 123(2), 468 (1979)

    ADS  Google Scholar 

  33. A. M. Shirokov, N. A. Smirnova, and Yu. F. Smirnov, Parameter symmetry of the interacting boson model, Phys. Lett. B 434(3–4), 237 (1998)

    ADS  Google Scholar 

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

    Google Scholar 

  35. D. D. Warner, and R. F. Casten, Predictions of the interacting boson approximation in a consistent Q framework, Phys. Rev. C 28(4), 1798 (1983)

    ADS  Google Scholar 

  36. P. O. Lipas, P. Toivonen, and D. D. Warner, IBA consistent-Q formalism extended to the vibrational region, Phys. Lett. B 155(5–6), 295 (1985)

    ADS  Google Scholar 

  37. R. F. Casten, Status of experimental tests of the IBA, in: Interacting Bose–Fermi Systems in Nuclei, edited by F. Iachello, Plenum, New York, 1981, page 3

    Google Scholar 

  38. P. Cejnar and J. Jolie, Dynamical-symmetry content of transitional IBM-1 hamiltonians, Phys. Lett. B 420(3–4), 241 (1998)

    ADS  Google Scholar 

  39. Y. Alhassid and A. Leviatan, Partial dynamical symmetry, J. Phys. A 25(23), L1265 (1992)

    ADS  MathSciNet  MATH  Google Scholar 

  40. A. Leviatan, Partial dynamical symmetry in deformed nuclei, Phys. Rev. Lett. 77(5), 818 (1996)

    ADS  Google Scholar 

  41. A. Leviatan, A. Novoselsky, and I. Talmi, O(5) symmetry in IBA-1 — the O(6)–U(5) transition region, Phys. Lett. B 172(2), 144 (1986)

    ADS  Google Scholar 

  42. P. Van Isacker, Dynamical symmetry and higher-order interactions, Phys. Rev. Lett. 83(21), 4269 (1999)

    ADS  Google Scholar 

  43. A. Leviatan and P. Van Isacker, Generalized partial dynamical symmetry in nuclei, Phys. Rev. Lett. 89(22), 222501 (2002)

    ADS  Google Scholar 

  44. A. Leviatan, Partial dynamical symmetries, Prog. Part. Nucl. Phys. 66(1), 93 (2011)

    ADS  Google Scholar 

  45. C. Kremer, J. Beller, A. Leviatan, N. Pietralla, G. Rainovski, R. Trippel, and P. Van Isacker, Linking partial and quasi dynamical symmetries in rotational nuclei, Phys. Rev. C 89, 041302(R) (2014)

    ADS  Google Scholar 

  46. F. Pan and J. P. Draayer, New algebraic solutions for SO(6) ↔ U(5) transitional nuclei in the interacting boson model, Nucl. Phys. A 636(2), 156 (1998)

    ADS  Google Scholar 

  47. D. J. Rowe, P. Rochford, and J. Repka, Dynamic structure and embedded representation in physics: The group theory of the adiabatic approximation, J. Math. Phys. 29(3), 572 (1988)

    ADS  MathSciNet  MATH  Google Scholar 

  48. D. J. Rowe, C. Bahri, and W. Wijesundera, Exactly solvable model of a superconducting to rotational phase transition, Phys. Rev. Lett. 80(20), 4394 (1998)

    ADS  Google Scholar 

  49. C. Bahri and D. J. Rowe, SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions, Nucl. Phys. A 662(1–2), 125 (2000)

    ADS  Google Scholar 

  50. M. Macek, J. Dobeš, and P. Cejnar, Transition from γ-rigid to γ-soft dynamics in the interacting boson model: Quasicriticality and quasidynamical symmetry, Phys. Rev. C 80(1), 014319 (2009)

    ADS  Google Scholar 

  51. D. Bonatsos, E. A. McCutchan, and R. F. Casten, SU(3) quasidynamical symmetry underlying the Alhassid–Whelan arc of regularity, Phys. Rev. Lett. 104(2), 022502 (2010)

    ADS  Google Scholar 

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Acknowledgements

I wish, on the occasion of the 88th anniversary of his birthday, to express my sincere thanks to Akito Arima for many years of stimulating discussions and his continual inspiration of my research. Many thanks are due to Amiram Leviatan and José-Enrique García-Ramos, in collaboration with whom many of the results reported in this contribution have been obtained.

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  1. Grand Accélérateur National d’Ions Lourds, CEA/DRF–CNRS/IN2P3 Bd Henri Becquerel, BP 55027, F-14076, Caen, France

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Van Isacker, P. Symmetries of the interacting boson model. Front. Phys. 13, 132107 (2018). https://doi.org/10.1007/s11467-018-0833-8

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