Advertisement

Frontiers of Physics

, 13:132114 | Cite as

Regularity of atomic nuclei with random interactions: sd bosons

  • Y. M. Zhao
Review Article
  • 7 Downloads
Part of the following topical collections:
  1. Simplicity, Symmetry, and Beauty of Atomic Nuclei

Abstract

Atomic nuclei are complex systems with gigantic configuration spaces, therefore truncations of model spaces are indispensable. Due to the short-range nature of the nuclear interactions, one may resort to a truncation by using coherent nucleon-pairs which are conveniently further simplified as bosons, such as sd bosons. The discovery of the spin-zero ground state dominance with random two-body interactions led to a series of studies on regular structure for sd bosons in the presence of random interactions, and this review article summarizes studies along this line in last two decades. We concentrate on various patterns exhibited in sd boson systems, and demonstrate that many random samples which were thought to be noisy exhibit very regular patterns, some of which are interpreted in terms of the U(5), O(6), \(\overline {O\left( 6 \right)} \), SU(3), and \(\overline {SU\left( 3 \right)} \) dynamical symmetries of the sd interacting boson model.

Keywords

regularity random interactions sd bosons 

Notes

Acknowledgements

We thank Professor Arima Akito for his collaboration and constant encouragements in studies summarized in this paper, and many other works such as the nucleon-pair approximations, systematics of nuclear masses, and algebraic studies of angular momentum. He is one of the co-authors in most of these papers; without him many of these studies would not likely be performed. We thank the National Natural Science Foundation of China under Grant No. 11675101, Shanghai Key Laboratory (Grant No. 11DZ2260700), and the Program of Shanghai Academic/Technology Research Leader (Grant No. 16XD1401600) for financial support.

References

  1. 1.
    C. W. Johnson, G. F. Bertsch, and D. J. Dean, Orderly spectra from random interactions, Phys. Rev. Lett. 80(13), 2749 (1998)ADSGoogle Scholar
  2. 2.
    C. Johnson, G. Bertsch, D. Dean, and I. Talmi, Generalized seniority from random Hamiltonians, Phys. Rev. C 61(1), 014311 (1999)ADSGoogle Scholar
  3. 3.
    D. Mulhall, A. Volya, and V. Zelevinsky, Geometric chaoticity leads to ordered spectra for randomly interacting fermions, Phys. Rev. Lett. 85(19), 4016 (2000)ADSGoogle Scholar
  4. 4.
    V. Zelevinsky and A. Volya, Nuclear structure, random interactions and mesoscopic physics, Phys. Rep. 391(3–6), 311 (2004)Google Scholar
  5. 5.
    Y. M. Zhao and A. Arima, Towards understanding the probability of 0+ ground states in even-even many-body systems, Phys. Rev. C 64(4), 041301 (2001)ADSGoogle Scholar
  6. 6.
    P. Chau Huu-Tai, A. Frank, N. A. Smirnova, and P. Van Isacker, Geometry of random interactions, Phys. Rev. C 66(6), 061302 (2002)ADSGoogle Scholar
  7. 7.
    Y. M. Zhao, A. Arima, and N. Yoshinaga, Simple approach to the angular momentum distribution in the ground states of many-body systems, Phys. Rev. C 66(3), 034302 (2002)ADSGoogle Scholar
  8. 8.
    T. Papenbrock and H. A. Weidenmüller, Distribution of spectral widths and preponderance of spin-0 ground states in nuclei, Phys. Rev. Lett. 93(13), 132503 (2004)ADSGoogle Scholar
  9. 9.
    N. Yoshinaga, A. Arima, and Y. M. Zhao, Lowest bound of energies for random interactions and the origin of spin-zero ground state dominance in even-even nuclei, Phys. Rev. C 73(1), 017303 (2006)ADSGoogle Scholar
  10. 10.
    Y. M. Zhao, A. Arima, and N. Yoshinaga, Manybody systems interacting via a two-body random ensemble (I): Angular momentum distribution in the ground states, Phys. Rev. C 66(6), 064322 (2002)ADSGoogle Scholar
  11. 11.
    Y. M. Zhao, A. Arima, and N. Yoshinaga, Angular momentum distribution of the ground states in the presence of random interactions: Boson systems, Phys. Rev. C 68(1), 014322 (2003)ADSGoogle Scholar
  12. 12.
    Y. Lu, Y. M. Zhao, and A. Arima, Spin I ground state probabilities of integrable systems under random interactions, Phys. Rev. C 91(2), 027301 (2015)ADSGoogle Scholar
  13. 13.
    Y. M. Zhao, A. Arima, and N. Yoshinaga, Regularities of many-body systems interacting by a two-body random ensemble, Phys. Rep. 400(1), 1 (2004)ADSMathSciNetGoogle Scholar
  14. 14.
    H. A. Weidenmüller and G. E. Mitchell, Random matrices and chaos in nuclear physics: Nuclear structure, Rev. Mod. Phys. 81(2), 539 (2009)ADSGoogle Scholar
  15. 15.
    Y. M. Zhao, A. Arima, N. Shimizu, K. Ogawa, N. Yoshinaga, and O. Scholten, Patterns of the ground states in the presence of random interactions: Nucleon systems, Phys. Rev. C 70(5), 054322 (2004)ADSGoogle Scholar
  16. 16.
    T. Papenbrock and H. A. Weidenmüller, Abundance of ground states with positive parity, Phys. Rev. C 78(5), 054305 (2008)ADSGoogle Scholar
  17. 17.
    N. Shimizu and T. Otsuka, Ground state properties with a random two-body interaction, Prog. Theor. Phys. 118(3), 491 (2007)ADSGoogle Scholar
  18. 18.
    M. Horoi, A. Volya, and V. Zelevinsky, Random interactions, isospin, and the ground states of odd-A and odd-odd nuclei, Phys. Rev. C 66(2), 024319 (2002)Google Scholar
  19. 19.
    V. Velázquez, J. G. Hirsch, A. Frank, and A. P. Zuker, A study of randomness, correlations, and collectivity in the nuclear shell model, Phys. Rev. C 67(3), 034311 (2003)Google Scholar
  20. 20.
    C. W. Johnson and H. A. Nam, New puzzle for manybody systems with random two-body interactions, Phys. Rev. C 75(4), 047305 (2007)ADSGoogle Scholar
  21. 21.
    G. J. Fu, J. J. Shen, Y. M. Zhao, and A. Arima, Regularities in low-lying states of atomic nuclei with random interactions, Phys. Rev. C 91(5), 054319 (2015)ADSGoogle Scholar
  22. 22.
    G. J. Fu, L. Y. Jia, Y. M. Zhao, and A. Arima, Monopole pairing correlations with random interactions, Phys. Rev. C 96(4), 044306 (2017)ADSGoogle Scholar
  23. 23.
    Y. Lei, Z. Y. Xu, Y. M. Zhao, S. Pittel, and A. Arima, Emergence of generalized seniority in low-lying states with random interactions, Phys. Rev. C 83(2), 024302 (2011)ADSGoogle Scholar
  24. 24.
    G. J. Fu, L. Y. Jia, Y. M. Zhao, and A. Arima, Monopole pairing correlations with random interactions, Phys. Rev. C 96(4), 044306 (2017)ADSGoogle Scholar
  25. 25.
    M. W. Kirson and J. A. Mizrahi, Random interactions with isospin, Phys. Rev. C 76(6), 064305 (2007)ADSGoogle Scholar
  26. 26.
    M. Horoi, A. Volya, and V. Zelevinsky, Random interactions, isospin, and the ground states of odd-A and odd-odd nuclei, Phys. Rev. C 66(2), 024319 (2002)Google Scholar
  27. 27.
    Y. M. Zhao, A. Arima, and N. Yoshinaga, Many-body systems interacting via a two-body random ensemble. I. Angular momentum distribution in the ground states, Phys. Rev. C 66(6), 064322 (2002)ADSGoogle Scholar
  28. 28.
    A. Arima and F. Iachello, Interacting boson model of collective states I: The vibrational limit, Ann. Phys. 99(2), 253 (1976)ADSGoogle Scholar
  29. 29.
    A. Arima and F. Iachello, Interacting boson model of collective nuclear states II: The rotational limit, Ann. Phys. 111(1), 209 (1978)ADSGoogle Scholar
  30. 30.
    A. Arima and F. Iachello, Interacting boson model of collective nuclear states IV: The O(6) limit, Ann. Phys. 123(2), 468 (1979)ADSGoogle Scholar
  31. 31.
    M. G. Mayer, On closed shells in nuclei (II), Phys. Rev. 75(12), 1969 (1949)ADSGoogle Scholar
  32. 32.
    J. H. D. Jensen, J. Suess, and O. Haxel, Modellmäβige deutung der ausgezeichneten nucleonenzahlen im kernbau, Naturwissenschaften 36(5), 155 (1949)ADSGoogle Scholar
  33. 33.
    O. Haxel, J. H. D. Jensen, and H. E. Suess, On the “magic numbers” in nuclear structure, Phys. Rev. 75(11), 1766 (1949)ADSGoogle Scholar
  34. 34.
    A. Bohr and B. R. Mottelson, Nuclear Structure, Volumes I and II, Benjamin, New York; World Scientific, Singapore, 1998Google Scholar
  35. 35.
    F. Iachello and A. Arima, The Interacting Boson Model, Cambridge University Press, 1987Google Scholar
  36. 36.
    R. Bijker and A. Frank, Band structure from random interactions, Phys. Rev. Lett. 84(3), 420 (2000)ADSGoogle Scholar
  37. 37.
    Y. M. Zhao, J. L. Ping, and A. Arima, Collectivity of low-lying states under random two-body interactions, Phys. Rev. C 76(5), 054318 (2007)ADSGoogle Scholar
  38. 38.
    J. N. Ginocchio, An exact fermion model with monopole and quadrupole pairing, Phys. Lett. B 79, 173 (1978)ADSGoogle Scholar
  39. 39.
    J. N. Ginocchio, On a generalization of quasispin to onopole and quadrupole pairing, Phys. Lett. B 85, 9 (1979)ADSGoogle Scholar
  40. 40.
    J. N. Ginocchio, A schematic model for monopole and quadrupole pairing in nuclei, Ann. Phys. 126(1), 234 (1980)ADSMathSciNetGoogle Scholar
  41. 41.
    C. L. Wu, X. G. Chen, J. Q. Chen, and M. W. Guidry, Fermion dynamical symmetry model of nuclei: Basis, Hamiltonian, and symmetries, Phys. Rev. C 36(3), 1157 (1987)MathSciNetGoogle Scholar
  42. 42.
    C. L. Wu, D. H. Feng, and M. W. Guidry, The fermion dynamical symmetry model, Adv. Nucl. Phys. 21, 227 (1994)Google Scholar
  43. 43.
    R. Bijker and A. Frank, Collective states in nuclei and many-body random interactions, Phys. Rev. C 62(1), 014303 (2000)ADSGoogle Scholar
  44. 44.
    N. Yoshida, Y. M. Zhao, and A. Arima, Proton-neutron interacting boson model under random two-body interactions, Phys. Rev. C 80(6), 064324 (2009)ADSGoogle Scholar
  45. 45.
    T. Otsuka, A. Arima, F. Iachello, and I. Talmi, Shell model description of interacting bosons, Phys. Lett. B 76(2), 139 (1978)ADSGoogle Scholar
  46. 46.
    C. W. Johnson, Orderly spectra from random interactions: Robust results, Rev. Mex. Fis. 45(S2), 25 (1999)Google Scholar
  47. 47.
    Y. M. Zhao, S. Pittel, R. Bijker, A. Frank, and A. Arima, Generic rotation in a collective SD nucleon-pair subspace, Phys. Rev. C 66(4), 041301 (2002)ADSGoogle Scholar
  48. 48.
    C. A. Mallmann, System of levels in even-even nuclei, Phys. Rev. Lett. 2(12), 507 (1959)ADSGoogle Scholar
  49. 49.
    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)ADSMathSciNetGoogle Scholar
  50. 50.
    A. E. L. Dieperink, O. Scholten, and F. Iachello, Classical limit of the interacting-boson model, Phys. Rev. Lett. 44(26), 1747 (1980)ADSGoogle Scholar
  51. 51.
    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)ADSMathSciNetzbMATHGoogle Scholar
  52. 52.
    T. Otsuka, A. Arima, and F. Iachello, Nuclear shell model and interacting bosons, Nucl. Phys. A 309(1–2), 1 (1978)ADSGoogle Scholar
  53. 53.
    K. Nomura, N. Shimizu, D. Vretenar, T. Niksic, and T. Otsuka, Robust regularity in g-soft nuclei and its microscopic realization, Phys. Rev. Lett. 108(13), 132501 (2012)ADSGoogle Scholar
  54. 54.
    R. Bijker and A. Frank, Mean-field analysis of interacting boson models with random interactions, Phys. Rev. C 64(6), 061303 (2001)ADSGoogle Scholar
  55. 55.
    F. Iachello, Algebraic methods for molecular rotationvibration spectra, Chem. Phys. Lett. 78(3), 581 (1981)ADSMathSciNetGoogle Scholar
  56. 56.
    F. Iachello and R. D. Levine, Algebraic approach to molecular rotation-vibration spectra (I): Diatomic molecules, J. Chem. Phys. 77(6), 3046 (1982)ADSMathSciNetGoogle Scholar
  57. 57.
    R. Bijker and A. Frank, Regular spectra in the vibron model with random interactions, Phys. Rev. C 65(4), 044316 (2002)ADSGoogle Scholar
  58. 58.
    Y. Lei, Y. M. Zhao, N. Yoshida, and A. Arima, Correlations of excited states for SD bosons in the presence of random interactions, Phys. Rev. C 83(4), 044302 (2011)ADSGoogle Scholar
  59. 59.
    Y. Lu, Y. M. Zhao, N. Yoshida, and A. Arima, Correlations between low-lying yrast states for s d bosons with random interactions, Phys. Rev. C 90(6), 064313 (2014)ADSGoogle Scholar
  60. 60.
    G. J. Fu, Y. M. Zhao, J. L. Ping, and A. Arima, Excited states of many-body systems in the fermion dynamical symmetry model with random interactions, Phys. Rev. C 88(3), 037302 (2013)ADSGoogle Scholar
  61. 61.
    G. J. Fu, Y. M. Zhao, and A. Arima, Regularities of low-lying states with random interactions in the fermion dynamical symmetry model, Phys. Rev. C 90(6), 064320 (2014)ADSGoogle Scholar
  62. 62.
    G. J. Fu, Y. Zhang, Y. M. Zhao, and A. Arima, Collective modes of low-lying states in the interacting boson model with random interactions, Phys. Rev. C 98(3), 034301 (2018)Google Scholar
  63. 63.
    R. F. Casten, edited by F. Iachello, Interacting Bose–Fermi Systems in Nuclei, Plenum, 1981Google Scholar
  64. 64.
    H. Ejiri, M. Ishihara, M. Sakai, K. Katori, and T. Inamura, Conversion electrons from (α, xn) reactions on Sm isotopes and nuclear structures of Gd nuclei, J. Phys. Soc. Jpn. 24(6), 1189 (1968)ADSGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Physics and AstronomyShanghai Jiaotong UniversityShanghaiChina

Personalised recommendations