Nuclear Low-lying Spectrum and Quantum Phase Transition

1. 第十三届全国核结构研讨会暨第九次全国 “核结构与量子力学”专题讨论会 Nuclear Low-lying Spectrum and Quantum Phase Transition 李志攀 西南大学物理科学与技术学院

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

3. Nuclear Low-lying Spectrum • Nuclear low-lying spectrum is an important physical quantity that can reveal rich structure information of atomic nuclei • Shape and shape transition 9- 8+ 7- 5- 6+ 3- 4+ 1- 2+ 0+

4. Nuclear Low-lying Spectrum • Nuclear low-lying spectrum is an important physics quantity that can reveal rich structure information of atomic nuclei • Shape and shape transition • Evolution of the shell structure T. Baumann Nature06213(2007) Z N=28 N=20 N N=16

5. Nuclear Low-lying Spectrum • Nuclear low-lying spectrum is an important physics quantity that can reveal rich structure information of atomic nuclei • Shape and shape transition • Evolution of the shell structure • Evidence for pairing correlation

6. Quantum Phase Transition in finite system Critical E • Quantum Phase Transition (QPT) : abrupt change of ground-state properties induced by variation of a non-thermal control parameter at zero temperature. • In atomic nuclei: • First and second order QPT can occur between systems characterized by different ground-state 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 F. Iachello, PRL2004 Deformed

7. Covariant Energy Density Functional (CEDF) Ring96, 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

8. Brief Review of the model Coll. Potential Moments of inertia Mass parameters Diagonalize: Nuclear spectroscopy T. Niksic, Z. P. Li, D. Vretenar, L. Prochniak, J. Meng, and P. Ring 79, 034303 (2009)

9. 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)]

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

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

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

13. 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

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

15. 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 • are 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)

16. 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.

17. 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

18. Second order QPT • PESs of Ba isotopes

19. Second order QPT • PESs of Xe isotopes

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

21. Second order QPT • Spectrum of 134Ba • Microscopic predictions are consistent 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

22. Summary • 5D Collective Hamiltonian based on • CEDF has been constructed • 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.

23. Summary • 5D Collective Hamiltonian based on • CEDF has been constructed • 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.

24. Summary • 5D Collective Hamiltonian based on • CEDF has been constructed • 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.

25. Summary • 5D Collective Hamiltonian based on • CEDF has been constructed • 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.

26. Outlook • Further application: • Systematic investigation of nuclear QPT • Shape coexistence, e.g. Kr & Pb • …… • Development of the model: • Cranking CEDF: Thouless-Valatin moment of inertia • Constraint on collective P: mass parameters • Coupling between nuclear shape oscillations and • pairing vibrations

27. Acknowledgments 孟杰教授, 张双全博士及北大JCNP全体成员 （北京大学） 赵恩广研究员, 周善贵研究员 （中科院理论物理研究所） 龙文辉教授 （兰州大学） 尧江明教授 （西南大学） 孙保华博士 （北京航空航天大学） 彭婧博士 （北京师范大学） 王守宇博士，亓斌博士 （山东大学） 张炜博士 （河南理工大学） Prof. D.Vretenar，Dr. T.Niksic，Prof. N.Paar（Zagreb, Croatia） Prof. P. Ring (TUM, Germany) Prof. J.Libert, Prof. E.Khan, Prof. N. Van Giai（IPN-Orsay, France） Prof. G. Lalazissis (Thessaloniki, Greece) Prof. G. Hillhouse (Stellenbosch, South Africa) Prof. L. Prochniak (Lublin, Poland) Prof. L. N. Savushkin (St. Petersburg, Russia)

28. Thank you For your attention

29. Collective Hamiltonian

30. Collective Parameter

31. Collective Parameter

32. Collective Parameter

33. Numerical Details E Spherical • Numerical solution of 5D Hamiltonian β Both the excited energy and BE2 are perfectly reproduced

34. Numerical Details • Convergence of the collective parameters For the medium heavy nuclei, N=14 can give convergent result

36. Shape fluctuation