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Nuclear Low-lying Spectrum and Quantum Phase Transition

17th Nuclear Physics Workshop, Kazimierz Dolny, Poland. Nuclear Low-lying Spectrum and Quantum Phase Transition. Zhipan Li School of Physical Science and Technology Southwest University. 1. 4. 2. 3. Introduction. Results and discussion. Summary and outlook.

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Nuclear Low-lying Spectrum and Quantum Phase Transition

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  1. 17th Nuclear Physics Workshop, Kazimierz Dolny, Poland Nuclear Low-lying Spectrum and Quantum Phase Transition Zhipan Li School of Physical Science and Technology Southwest University

  2. 1 4 2 3 Introduction Results and discussion Summary and outlook Theoretical framework Outline

  3. Quantum Phase Transition in finite system Critical E • Quantum Phase Transition (QPT) between competing ground-state phases induced by variation of a non-thermal control parameter at zero temperature. • In atomic nuclei: • 1st and 2nd order QPT: abrupt transition in shapes. • Control Par. Number of nucleons • Two approaches to study QPT • Method of Landau based on potentials (not observables) • Direct computation of order parameters (integer con. par.) • Combine both approaches in a self-consistent microscopic framework Spherical Potential Order par. β P. Cejnar et al., RMP82, 2155 (2010) F. Iachello, PRL2004 Deformed

  4. Covariant Energy Density Functional (CEDF) Ring1996, Vretenar2005, Meng2006 • CEDF: nuclear structure over almost the whole nuclide chart • Scalar and vector fields: nuclear saturation properties • Spin-orbit splitting • Origin of the pseudo-spin symmetry • Spin symmetry in anti-nucleon spectrum • …… • Spectrum: beyond the mean-field approximation • Restoration of broken symmetry, e.g. rotational • Mixing of different shape configurations AMP+GCM: Niksic2006, Yao2010 PES 5D Collective Hamiltonian based on CEDF

  5. Brief Review of the model Coll. Potential Moments of inertia Mass parameters Diagonalize: Nuclear spectroscopy Libert, Girod & Delaroche, PRC60, 054301 (99) Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, 034303 (09) Prochniak & Rohozinski, JPG36, 123101 (09)

  6. Microscopic Analysis of nuclear QPT • Spherical to prolate 1st order QPT • [Z.P. Li, T. Niksic, D. Vretenar, J. Meng, G.A. Lalazissis, P. Ring, PRC79, 054301(2009)] • Analysis of order parameter • [Z.P. Li, T. Niksic, D. Vretenar, J. Meng, PRC80, 061301(R) (2009)] • Spherical to γ-unstable 2nd order QPT • [Z.P. Li, T. Niksic, D. Vretenar, J. Meng, PRC81, 034316 (2010)]

  7. First order QPT • Potential Energy Surfaces (PESs) Discontinuity

  8. First order QPT • Potential Energy Surfaces (PESs) along β along γ

  9. First order QPT • Spectrum detailed spectroscopy has been reproduced well !!

  10. First order QPT • Spectrum • Characteristic features: X(5) Sharp increase of R42=E(41)/E(21) and B(E2; 21→01) in the yrast band

  11. First order QPT • Single-particle levels 150Nd

  12. Microscopic analysis of Order parameters F. Iachello, PRL2004 based on IBM • Finite size effect (nuclei as mesoscopic systems) • Microscopic signatures (order parameter) • In finite systems, the discontinuities of QPT • will be smoothed out • 1st order 2nd order; 2nd order crossover • Isotope shift & isomer shift • Sharp peak at N~90 in (a) • Abrupt decrease; change sign in (b)

  13. Microscopic analysis of Order parameters • Microscopic signatures (order parameter) Conclusion: even though the control parameter is finite number of nucleons, the phase transition does not appear to be significantly smoothed out by the finiteness of the nuclear system.

  14. Second order QPT • Are the remarkable results for 1st order QPT accidental ? • Can the same EDF describe other types of QPT in different mass regions ? R. Casten, PRL2000 F. Iachello, PRL2000

  15. Second order QPT • PESs of Ba isotopes

  16. Second order QPT • PESs of Xe isotopes

  17. Second order QPT • Evolution of shape fluctuation: Δβ/〈β〉, Δγ/〈γ〉

  18. Second order QPT • Spectrum of 134Ba • Microscopic predictions consist with data and E(5) for g.s. band • Sequence of 22, 31, 42 : well structure / ~0.3 MeV higher • The order of two excited 0+ states is reversed

  19. Summary and outlook • Microscopic analysis of nuclear QPT • PESs display clear shape transitions • The spectrum and characteristic features have been • reproduced well for both 1st & 2nd order QPT • The microscopic signatures have shown that the phase • transition does not appear to be significantly smoothed • out by the finiteness of nuclear system. • Further development of the model: • Time-odd part for inertia parameters • Coupling between the pairing & quadruple vibration

  20. Thank You ! J. Meng & JCNP group D. Vretenar & T. Niksic P. Ring L. Prochniak G. A. Lalazissis

  21. Collective Hamiltonian

  22. Collective Parameter

  23. Collective Parameter

  24. Collective Parameter

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