Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

Article

Abstract

We study systematically the evolutive behaviors of some energy ratios, E2 transition rate ratios and isomer shift in the nuclear shape phase transitions. We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition, similar to that in the second order phase transition.

Keywords

nuclear shape phase transition critical point particle number scaling behavior interacting boson model 

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References

  1. 1.
    Ginocchio J N, Kirson M W. Relationship between the Bohr collective Hamiltonian and the interacting-boson model. Phys Rev Lett, 1980, 44: 1744–1747CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Dieperink A E L, Scholten O, Iachello F. Classical limit of the interacting-boson model. Phys Rev Lett, 1980, 44: 1747–1750CrossRefADSGoogle Scholar
  3. 3.
    Feng D H, Gilmore R, Deans S R. Phase-transitions and the geometric-properties of the interacting boson model. Phys Rev C, 1981, 23: 1254–1258CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Van Isacker P, Chen J Q. Classical limit of the interacting boson Hamiltonian. Phys Rev C, 1981, 24: 684–689CrossRefADSGoogle Scholar
  5. 5.
    Warner D D, Casten R F. Revised formulation of the phenomenological interacting boson model. Phys Rev Lett, 1982, 48: 1385–1389; Predictions of the interacting boson approximation in a consistent-Q framework. Phys Rev C, 1983, 28: 1798–1806CrossRefADSGoogle Scholar
  6. 6.
    Leviatan A. Partial dynamical symmetry in deformed nuclei. Phys Rev Lett, 1996, 77: 818–821; Leviatan A, Van Isacker P. Generalized partial dynamical symmetry in nuclei. Phys Rev Lett, 2002, 89: 222501; Leviatan A. Partial dynamical symmetry at critical points of quantum phase transitions. Phys Rev Lett, 2007, 98: 242502CrossRefADSGoogle Scholar
  7. 7.
    Warner D. Nuclear physics—A triple point in nuclei. Nature, 2002, 420: 614–615CrossRefADSGoogle Scholar
  8. 8.
    Jolie J, Cejnar P, Casten R F, et al. Triple point of nuclear deformations. Phys Rev Lett, 2002, 89: 182502Google Scholar
  9. 9.
    Iachello F, Zamfir N V. Quantum phase transitions in mesoscopic systems. Phys Rev Lett, 2004, 92: 212501Google Scholar
  10. 10.
    Rowe D J. Quasidynamical symmetry in an interacting boson model phase transition. Phys Rev Lett, 2004, 93: 122502Google Scholar
  11. 11.
    Rowe D J, Turner P S, Rosensteel G. Scaling properties and asymptotic spectra of finite models of phase transitions as they approach macroscopic limits. Phys Rev Lett, 2004, 93: 232502Google Scholar
  12. 12.
    Cejnar P, Heinze S, Dobeš J. Thermodynamic analogy for quantum phase transitions at zero temperature. Phys Rev C, 2005, 71: 011304(R)Google Scholar
  13. 13.
    Liu Y X, Mu L Z, Wei H Q. Approach to the rotation driven vibrational to axially rotational shape phase transition along the yrast line of a nucleus. Phys Lett B, 2006, 633: 49–53; Zhao Y, Liu Y, Mu L Z, et al. Rotational driven nuclear shape phase transition of the yrast states of individual nucleus in interacting boson model. Int J Mod Phys E, 2006, 15: 1711–1721CrossRefADSGoogle Scholar
  14. 14.
    Casten R F. Shape phase transitions and critical-point phenomena in atomic nuclei. Nat Phys, 2006, 2: 811–820; Casten R F, McCutchan E A. Quantum phase transitions and structural evolution in nuclei. J Phys G, 2007, 34: R285–R320; Casten R F. Quantum phase transitions and structural evolution in nuclei. Prog Part Nucl Phys, 2009, 62: 183–209CrossRefGoogle Scholar
  15. 15.
    Cejnar P, Jolie J. Quantum phase transitions in the interacting boson model. Prog Part Nucl Phys, 2009, 62: 210–256CrossRefADSGoogle Scholar
  16. 16.
    Hwiok S, Heenen P-H, Nazarewicz W. Shape coexistence and triaxiality in the superheavy nuclei. Nature, 2005, 433: 705–709CrossRefADSGoogle Scholar
  17. 17.
    Meng J, Zhang W, Zhang S Q, et al. Shape evolution for Sm isotopes in relativistic mean-field theory. Eur Phys J A, 2005 25: 23–27; Nikšić T, Vretenar D, Lalazissis G A, et al. Microscopic description of nuclear quantum phase transitions. Phys Rev Lett, 2007, 99: 092502CrossRefGoogle Scholar
  18. 18.
    Iachello F, Levine R D. Algebraic Theory of Molecules. Oxford: Oxford University, 1995Google Scholar
  19. 19.
    Kuyucak S. Shape-phase transitions in the vibron model and bent molecules. Chem Phys Lett, 1999, 301: 435–440CrossRefADSGoogle Scholar
  20. 20.
    Pérez-Bernal F, Santos L F, Vaccaro P H, et al. Spectroscopic signatures of nonrigidity: Algebraic analyses of infrared and Raman transitions in nonrigid species. Chem Phys Lett, 2005, 414: 398–404CrossRefADSGoogle Scholar
  21. 21.
    Yépez-Martínez H, Cseh J, Hess P O. Phase transitions in algebraic cluster models. Phys Rev C, 2006, 74: 024319Google Scholar
  22. 22.
    Feshbach F, Iachello F. Interacting boson model structure of O–16. Phys Lett B, 1973, 45: 7–11; Feshbach F, Iachello F. Interacting boson model. Ann Phys (N.Y.), 1974, 84: 211–231; Iachello F, Arima A. Boson symmetries in vibrational nuclei. Phys Lett B, 1974, 53: 309–312; Arima A, Iachello F. Collective nuclear states as representations of a SU(6) group. Phys Rev Lett, 1975, 35: 1069–1072; Arima A, Iachello F. Interacting boson model of collective states 1: Vibrational limit. Ann Phys (N.Y.), 1976, 99: 253–317; Arima A, Iachello F. Interacting boson model of collective states 2: Rotational limit. Ann Phys (N.Y.), 1978, 111: 201–238; Scholten O, Iachello F, Arima A. Interacting boson model of collective states 3: Transition from SU(5) to SU(3). Ann Phys (N.Y.), 1978, 115: 325–366; Arima A, Iachello F. Interacting boson model of collective states 4: O(6) limit. Ann Phys (N.Y.), 1979, 123: 468–492CrossRefADSGoogle Scholar
  23. 23.
    Iachello F, Arima A. The Interacting Boson Model. Cambridge: Cambridge University Press, 1987Google Scholar
  24. 24.
    Iachello F. Dynamic symmetries at the critical point. Phys Rev Lett, 2000, 85: 3580–3583CrossRefADSGoogle Scholar
  25. 25.
    Leviatan A, Ginocchio J N. Critical-point symmetry in a finite system. Phys Rev Lett, 2003, 90: 212501Google Scholar
  26. 26.
    Iachello F. Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition. Phys Rev Lett, 2001, 87: 052502Google Scholar
  27. 27.
    Casten R F, Zamfir N V. Evidence for a possible E(5) symmetry in Ba-134. Phys Rev Lett, 2000, 85: 3584-3587Google Scholar
  28. 28.
    Frank A, Alonso C E, Arias J M. Search for E(5) symmetry in nuclei: The Ru isotopes. Phys Rev C, 2002, 65: 014301Google Scholar
  29. 29.
    Zhang D L, Liu Y X. Empirical example of possible E(5) symmetry nucleus 108Pd. Phys Rev C, 2002, 65: 057301; Zhang D L, Liu Y X. Evidence for a possible E(5) symmetry in 130Xe. Chin Phys Lett, 2003, 20: 1028–1030; Clark R M, Cromaz M, Deleplanque M A, et al. Searching for E(5) behavior in nuclei. Phys Rev C, 2004, 69: 064322; von Garrel H, von Brentano P, Fransen C, et al. Low-lying E1, M1, and E2 strength distributions in 124,126,129,130,132,134,136Xe: Systematic photon scattering experiments in the mass region of a nuclear shape or phase transition. Phys Rev C, 2006, 73: 054315Google Scholar
  30. 30.
    Casten R F, Zamfir N V. Empirical realization of a critical point description in atomic nuclei. Phys Rev Lett, 2001, 87: 052503Google Scholar
  31. 31.
    Krücken R, Albanna B, Bialik C, et al. B(E2) values in 150Nd and the critical point symmetry X(5). Phys Rev Lett, 2002, 88: 232501; Zhang D L, Zhao H Y. Empirical example of nucleus with transitional dynamical symmetry X(5). Chin Phys Lett, 2002, 19: 779–781; Hutter C, Krücken R, Aprahamian A, et al. B(E2) values and the search for the critical point symmetry X(5) in 104M and 106Mo. Phys Rev C, 2003, 67: 054315; Möller O, Dewald A, Petkov P, et al. Electromagnetic transition strengths in 156Dy. Phys Rev C, 2006, 74: 024313; Mertz A F, McCutchan E A, Casten R F, et al. First experimental test of X(5) critical-point symmetry in the A 130 mass region: Low-spin states and the collective structure of 130Ce. Phys Rev C, 2008, 77: 014307Google Scholar
  32. 32.
    Tonev D, Dewald A, Klug T, et al. Transition probabilities in 154Gd: Evidence for X(5) critical point symmetry. Phys Rev C, 2004, 69: 034334; Dewald A, Möller O, Tonev D, et al. Shape changes and test of the critical-point symmetry X(5) in N = 90 nuclei. Eur Phys J A, 2004, 20: 173–178Google Scholar
  33. 33.
    Zhang Y, Hou Z F, Liu Y X. Distinguishing a first order from a second order nuclear shape phase transition in the interacting boson model. Phys Rev C, 2007, 76: 011305(R)Google Scholar
  34. 34.
    Bonatsos D, McCutchan E A, Casten R F, et al. Simple empirical order parameter for a first-order quantum phase transition in atomic nuclei. Phys Rev Lett, 2008, 100: 142501Google Scholar
  35. 35.
    Dusuel S, Vidal J, Arias J M, et al. Finite-size scaling exponents in the interacting boson model. Phys Rev C, 2005, 72: 011301(R); Dusuel S, Vidal J, Arias J M, et al. Continuous unitary transformations in two-level boson systems. Phys Rev C, 2005, 72: 064332Google Scholar
  36. 36.
    Arias J M, Dukelsky J, García-Ramos J E, et al. Two-level interacting boson models beyond the mean field. Phys Rev C, 2007, 75: 014301Google Scholar
  37. 37.
    Zhang Y, Hou Z F, Chen H, et al. Quantum phase transition in the U(4) vibron model and the E(3) symmetry. Phys Rev C, 2008, 78: 024314Google Scholar
  38. 38.
    Pan F, Zhang Y, Draayer J P. Quantum phase transitions in the U(5)-O(6) large-N limit. J Phys G, 2005, 31: 1039–1042CrossRefADSGoogle Scholar
  39. 39.
    Liu Y X, Hou Z F, Zhang Y. Some aspects of shape phase transition in even-even nuclei. Int J Mod Phys E, 2008, 17(Suppl): 352–372CrossRefADSGoogle Scholar
  40. 40.
    Iachello F, Van Isacker P. The interacting Boson-Fermion Model. Cambridge: Cambridge University Press, 1991Google Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  2. 2.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy Ion AcceleratorLanzhouChina

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