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Nuclear collectivity in the even–even \(^{164{-}178}\)Yb along the yrast line

  • Hui-Fang Li
  • Hua-Lei Wang
  • Min-Liang Liu
Article
  • 26 Downloads

Abstract

The collective properties along the yrast line in well-deformed even–even \(^{164{-}178}\) Yb isotopes are investigated by pairing self-consistent total Routhian surface (TRS) calculations and extended E-gamma over spin (E-GOS) curves. The calculated results from ground-state deformations, e.g., \(\beta _2\), are in agreement with previous theoretical predictions and available experimental data. The basic behaviors of moment of inertia are reproduced by the present TRS calculations and discussed based on the aligned angular momenta. The centipede-like E-GOS curves indicate that the non-rotational components appear along the yrast sequences in these nuclei, which can explain the discrepancy in the moment of inertia between theory and experiment to some extent. The further extended E-GOS curves, which include the first-order rotation–vibration coupling, appear to provide possible evidence of vibrational effects in the well-deformed nuclei of \(^{164{-}178}\)Yb.

Keywords

Vibrational effect Total Routhian surface calculation E-GOS curve 

References

  1. 1.
    R. Lucas, Nuclear shapes. Europhys. News 32, 5 (2001).  https://doi.org/10.1051/epn:2001101 CrossRefGoogle Scholar
  2. 2.
    Nationl Nuclear Data Center. http://www.nndc.bnl.gov/. Accessed 20 Oct 2017
  3. 3.
    W. Ogle, S. Wahlborn, R. Piepenbring et al., Single-particle levels of nonspherical nuclei in the region 150\(<A<\)190. Rev. Mod. Phys. 43, 424 (1971).  https://doi.org/10.1103/RevModPhys.43.424 CrossRefGoogle Scholar
  4. 4.
    S. Wahlborn, Effects of blocking on the level spacings of odd-mass deformed nuclei. Nucl. Phys. 37, 554 (1962).  https://doi.org/10.1016/0029-5582(62)90290-0 CrossRefGoogle Scholar
  5. 5.
    G. Ehrling, S. Wahlborn, Single-particle model calculations for deformed nuclei of spheroidal and non-spheroidal shapes. Phys. Scripta 6, 94 (1972).  https://doi.org/10.1088/0031-8949/6/2-3/002 CrossRefGoogle Scholar
  6. 6.
    W. Satuła, R. Wyss, P. Magierski et al., The Lipkin–Nogami formalism for the cranked mean field. Nucl. Phys. A 578, 45 (1994).  https://doi.org/10.1016/0375-9474(94)90968-7 CrossRefGoogle Scholar
  7. 7.
    F.R. Xu, W. Satuła, R. Wyss, Quadrupole pairing interaction and signature inversion. Nucl. Phys. A 669, 119 (2000).  https://doi.org/10.1016/S0375-9474(99)00817-9 CrossRefGoogle Scholar
  8. 8.
    Z.H. Zhang, X.T. He, J.Y. Zeng et al., Systematic investigation of the rotational bands in nuclei with \(Z\approx\)100 using a particle-number conserving method based on a cranked shell model. Phys. Rev. C 85, 014324 (2012).  https://doi.org/10.1103/PhysRevC.85.014324 CrossRefGoogle Scholar
  9. 9.
    K. Hara, Y. Sun, Projected shell model and high-spin spectroscopy. Int. J. Mod. Phys. E 4, 637 (1995).  https://doi.org/10.1142/S0218301395000250 CrossRefGoogle Scholar
  10. 10.
    Z. Shi, Z.H. Zhang, Q.B. Chen et al., Shell-model-like approach based on cranking covariant density functional theory: band crossing and shape evolution in \(^{60}\)Fe. Phys. Rev. C 97, 034317 (2018).  https://doi.org/10.1103/PhysRevC.97.034317 CrossRefGoogle Scholar
  11. 11.
    P.H. Regan, C.W. Beausang, N.V. Zamfir et al., Signature for vibrational to rotational evolution along the yrast line. Phys. Rev. Lett. 90, 152502 (2003).  https://doi.org/10.1103/PhysRevLett.90.152502 CrossRefGoogle Scholar
  12. 12.
    Q. Yang, H.L. Wang, M.L. Liu et al., Characteristics of collectivity along the yrast line in even–even tungsten isotopes. Phys. Rev. C 94, 024310 (2016).  https://doi.org/10.1103/PhysRevC.94.024310 CrossRefGoogle Scholar
  13. 13.
    J. Yang, H.L. Wang, Q.Z. Chai et al., Evolution of shape and rotational structure in neutron-deficient \(^{118-128}\)Ba nuclei. Prog. Theor. Exp. Phys. 2016, 063D03 (2016).  https://doi.org/10.1093/ptep/ptw074 CrossRefGoogle Scholar
  14. 14.
    H.Y. Meng, H.L. Wang, Q.Z. Chai et al., Possible properties on nuclear shape and stiffness evolution: a systematic analysis based on nuclear-energy-surface calculations. Nucl. Phys. Rev. 34, 481 (2017).  https://doi.org/10.11804/NuclPhysRev.34.03.481 CrossRefGoogle Scholar
  15. 15.
    Q.Z. Chai, W.J. Zhao, H.L. Wang et al., Possible observation of shape-coexisting configurations in even-even midshell isotones with \(N=104\): a systematic total Routhian surface calculation. Nucl. Sci. Tech. 29, 38 (2018).  https://doi.org/10.1007/s41365-018-0381-5 CrossRefGoogle Scholar
  16. 16.
    W. Nazarewicz, G.A. Leander, J. Dudek, Octupole shapes and shape changes at high spins in Ra and Th nuclei. Nucl. Phys. A 467, 437 (1987).  https://doi.org/10.1016/0375-9474(87)90539-2 CrossRefGoogle Scholar
  17. 17.
    R. Bengtsson, S. Frauendorf, Quasiparticle spectra near the yrast line. Nucl. Phys. A 327, 139 (1979).  https://doi.org/10.1016/0375-9474(79)90322-1 CrossRefGoogle Scholar
  18. 18.
    S. Frauendorf, Spin alignment in heavy nuclei. Phys. Scripta 24, 349 (1981).  https://doi.org/10.1088/0031-8949/24/1B/034 CrossRefGoogle Scholar
  19. 19.
    W.D. Myers, W.J. Swiatecki, Nuclear masses and deformations. Nucl. Phys. 81, 1 (1966).  https://doi.org/10.1016/0029-5582(66)90639-0 CrossRefGoogle Scholar
  20. 20.
    V.M. Strutinsky, Shell effects in nuclear masses and deformation energies. Nucl. Phys. A 95, 420 (1967).  https://doi.org/10.1016/0375-9474(67)90510-6 CrossRefGoogle Scholar
  21. 21.
    H.C. Pradhan, Y. Nogami, J. Law, Study of approximations in the nuclear pairing-force problem. Nucl. Phys. A 201, 357 (1973).  https://doi.org/10.1016/0375-9474(73)90071-7 CrossRefGoogle Scholar
  22. 22.
    P. Möller, J.R. Nix, Nuclear pairing models. Nucl. Phys. A 536, 20 (1992).  https://doi.org/10.1016/0375-9474(92)90244-E CrossRefGoogle Scholar
  23. 23.
    H. Sakamoto, T. Kishimoto, Origin of the multipole pairing interactions. Phys. Lett. B 245, 321 (1990).  https://doi.org/10.1016/0370-2693(90)90651-L CrossRefGoogle Scholar
  24. 24.
    Q.Z. Chai, W.J. Zhao, M.L. Liu et al., Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier. Chin. Phys. C 42, 5 (2018).  https://doi.org/10.1088/1674-1137/42/5/054101 CrossRefGoogle Scholar
  25. 25.
    C.A. Mallmann, System of levels in even-even nuclei. Phys. Rev. Lett. 2, 507 (1959).  https://doi.org/10.1103/PhysRevLett.2.507 CrossRefGoogle Scholar
  26. 26.
    S. Goriely, F. Tondeur, J.M. Pearson, A Hartree–Fock nuclear mass table. At. Data Nucl. Data Tables 77, 311 (2001).  https://doi.org/10.1006/adnd.2000.0857 CrossRefGoogle Scholar
  27. 27.
    Y. Aboussir, J.M. Pearson, A.K. Dutta et al., Nuclear mass formula via an approximation to the Hartree–Fock method. At. Data Nucl. Data Tables 61, 127 (1995).  https://doi.org/10.1016/S0092-640X(95)90014-4 CrossRefGoogle Scholar
  28. 28.
    S. Raman, C.W. Nestorjr, P. Tikkaned, Transition probability from the ground to the first-excited \(2^{+}\) state of even-even nuclides. At. Data Nucl. Data Tables 78, 1 (2001).  https://doi.org/10.1006/adnd.2001.0858 CrossRefGoogle Scholar
  29. 29.
    J. Dudek, W. Nazarewicz, P. Olanders, On the shape consistency in the deformed shell-model approach. Nucl. Phys. A 420, 285 (1984).  https://doi.org/10.1016/0375-9474(84)90443-3 CrossRefGoogle Scholar
  30. 30.
    N. Fouladi, J. Fouladi, H. Sabri, Investigation of low-lying energy spectra for deformed prolate nuclei via partial dynamical SU(3) symmetry. Eur. Phys. J. Plus 130, 112 (2015).  https://doi.org/10.1140/epjp/i2015-15112-7 CrossRefGoogle Scholar
  31. 31.
    R.F. Casten, D.S. Brenner, P.E. Haustein, Valence \(p\)-\(n\) interactions and the development of collectivity in heavy nuclei. Phys. Rev. Lett. 58, 658 (1987).  https://doi.org/10.1103/PhysRevLett.58.658 CrossRefGoogle Scholar
  32. 32.
    R.F. Casten, Possible unified interpretation of heavy nuclei. Phys. Rev. Lett. 54, 1991 (1985).  https://doi.org/10.1103/PhysRevLett.54.1991 CrossRefGoogle Scholar
  33. 33.
    R.F. Casten, \(N_{p}N_{n}\) systematics in heavy nuclei. Nucl. Phys. A 443, 1 (1985).  https://doi.org/10.1016/0375-9474(85)90318-5 CrossRefGoogle Scholar
  34. 34.
    R.F. Casten, N.V. Zamfir, The evolution of nuclear structure: the \(N_pN_n\) scheme and related correlations. J. Phys. G: Nucl. Part. Phys. 22, 1521 (1996).  https://doi.org/10.1088/0954-3899/22/11/002 CrossRefGoogle Scholar
  35. 35.
    M.A.J. Mariscotti, Rotational description of states in closed-and near-closed-shell nuclei. Phys. Rev. Lett. 24, 1242 (1970).  https://doi.org/10.1103/PhysRevLett.24.1242 CrossRefGoogle Scholar
  36. 36.
    J.B. Gupta, New perspective in rotation–vibration interaction. Int. J. Mod. Phys. E 22, 1350023 (2013).  https://doi.org/10.1142/S0218301313500237 CrossRefGoogle Scholar
  37. 37.
    A. Nordlund, R. Bengtsson, P. Ekströmp et al., Probing the limits of complete spectroscopy in \(^{164}\)Yb. Nucl. Phys. A 591, 117 (1995).  https://doi.org/10.1016/0375-9474(95)00124-J CrossRefGoogle Scholar
  38. 38.
    C.A. Fields, K.H. Hicks, R.J. Peterson, Band crossings at low rotational frequency in \(^{166}\)Yb. Nucl. Phys. A 431, 473 (1995).  https://doi.org/10.1016/0375-9474(84)90119-2 CrossRefGoogle Scholar
  39. 39.
    A. Fitzpatrick, S.Y. Araddad et al., Proton alignments at high rotational frequency in \(^{167,168}\)Yb. Nucl. Phys. A 582, 335 (1995).  https://doi.org/10.1016/0375-9474(94)00459-Z CrossRefGoogle Scholar
  40. 40.
    P.M. Walker, S.R. Faber, W.H. Bentley et al., Negative-parity yrast band in \(^{170}\)Yb: rotation-aligned neutrons with deformation-coupled bandhead? Phys. Lett. B 81, 9 (1979).  https://doi.org/10.1016/0370-2693(79)90608-7 CrossRefGoogle Scholar
  41. 41.
    S.J. Asztalos, I.Y. Lee, K. Vetter et al., Spin yields of neutron-rich nuclei from deep inelastic reactions. Phys. Rev. C 60, 044307 (1999).  https://doi.org/10.1103/PhysRevC.60.044307 CrossRefGoogle Scholar
  42. 42.
    I.Y. Lee, S. Asztalos, M.A. Deleplanque et al., Study of neutron-rich nuclei using deep-inelastic reactions. Phys. Rev. C 56, 753 (1997).  https://doi.org/10.1103/PhysRevC.56.753 CrossRefGoogle Scholar
  43. 43.
    H.L. Wang, Q.Z. Chai, J.G. Jiang et al., Rotational properties in even-even superheavy \(^{254-258}\)Rf nuclei based on total-Routhian-surface calculations. Chin. Phys. C 38, 7 (2014).  https://doi.org/10.1088/1674-1137/38/7/074101 CrossRefGoogle Scholar
  44. 44.
    F. Al-khudair, G.L. Long, Y. Sun, Competition in rotation-alignment between high-\(j\) neutrons and protons in transfermium nuclei. Phys. Rev. C 79, 034320 (2009).  https://doi.org/10.1103/PhysRevC.79.034320 CrossRefGoogle Scholar
  45. 45.
    P.M. Walker, P.O. Arve, J. Simpson et al., Double crossing in \(^{174}\)Hf: A deformation jump? Phys. Lett. B 168, 326 (1986).  https://doi.org/10.1016/0370-2693(86)91638-2 CrossRefGoogle Scholar
  46. 46.
    A. Bohr, Quadrupole degree of freedom for the nuclear shape. Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26, 1 (1952)Google Scholar
  47. 47.
    G. Andersson, S.E. Larsson, G. Leander et al., Nuclear shell structure at very high angular momentum. Nucl. Phys. A 268, 205 (1976).  https://doi.org/10.1016/0375-9474(76)90461-9 CrossRefGoogle Scholar
  48. 48.
    H.L. Wang, J. Yang, M.L. Liu et al., Evolution of ground-state quadrupole and octupole stiffnesses in even–even barium isotopes. Phys. Rev. C 92, 024303 (2015).  https://doi.org/10.1103/PhysRevC.92.024303 CrossRefGoogle Scholar
  49. 49.
    S.F. Shen, Y.B. Chen, F.R. Xu et al., Signature for rotational to vibrational evolution along the yrast line. Phys. Rev. C 75, 047304 (2007).  https://doi.org/10.1103/PhysRevC.75.047304 CrossRefGoogle Scholar

Copyright information

© China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Physics and EngineeringZhengzhou UniversityZhengzhouChina
  2. 2.Institute of Modern PhysicsChinese Academy of SciencesLanzhouChina

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