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

www.swu.edu.cn

Outline

1

Introduction

2

Theoretical framework

3

Results and discussion

4

Summary and outlook

Quantum Phase Transition in finite system



Quantum Phase Transition (QPT) between competing ground-state phases induced by variation of a non thermal control parameter at zero temperature. Critical



In atomic nuclei:



1 st and 2 nd order QPT:

abrupt transition in shapes.

 Control Par. Number of nucleons

E

Spherical Potential Order par.

 P. Cejnar et al., RMP82, 2155 (2010)

β

Deformed Two approaches to study QPT

 Method of Landau based on potentials (not observables)  Direct computation of order parameters (integer con. par.)

F. Iachello, PRL2004



Combine both approaches in a self-consistent microscopic framework

Covariant Energy Density Functional (CEDF)



CEDF: nuclear structure over almost the whole nuclide chart

Ring1996, Vretenar2005, Meng2006 

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 PES

AMP+GCM: Niksic2006, Yao2010 5D Collective Hamiltonian based on CEDF

Brief Review of the model

Coll. Potential Moments of inertia Mass parameters Construct 5D Collective Hamiltonian

(vib + rot)

Diagonalize: Nuclear spectroscopy Density Functional E(J π ), BE2 … Cal. Exp.

ph + pp

Libert, Girod & Delaroche, PRC60, 054301 (99) Prochniak & Rohozinski, JPG36, 123101 (09) Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, 034303 (09)

Microscopic Analysis of nuclear QPT



Spherical to prolate 1

st

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 2

nd

order QPT

[Z.P. Li, T. Niksic, D. Vretenar, J. Meng, PRC81, 034316 (2010)]

First order QPT 

Potential Energy Surfaces (PESs) Discontinuity

First order QPT 

Potential Energy Surfaces (PESs)

along β along γ

First order QPT 

Spectrum

detailed spectroscopy has been reproduced well !!

First order QPT 

Spectrum



Characteristic features: X(5) Sharp increase of R 42 =E(4 1 )/E(2 1 ) and B(E2; 2 1 →0 1 ) in the yrast band

First order QPT 

Single-particle levels

150 Nd

Microscopic analysis of Order parameters 

Finite size effect (nuclei as mesoscopic systems)



In finite systems, the discontinuities of QPT will be smoothed out



1 st order 2 nd order; 2 nd order crossover F. Iachello, PRL2004 based on IBM



Microscopic signatures (order parameter) 1. Isotope shift & isomer shift 2. Sharp peak at N~90 in (a) 3. Abrupt decrease; change sign in (b)

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.

Second order QPT 

Are the remarkable results for 1 st order QPT accidental ?



Can the same EDF describe other types of QPT in different mass regions ?

F. Iachello, PRL2000 R. Casten, PRL2000

Second order QPT 

PESs of Ba isotopes

Second order QPT 

PESs of Xe isotopes

Second order QPT 

Evolution of shape fluctuation: Δβ

/

〈 β 〉, Δγ

/

〈 γ 〉

Second order QPT 

Spectrum of 134 Ba

 Microscopic predictions consist with data and E(5) for g.s. band  Sequence of 2 2 , 3 1 , 4 2  : well structure / ~0.3 MeV higher The order of two excited 0+ states is reversed

Summary and outlook



Microscopic analysis of nuclear QPT



PESs display clear shape transitions



The spectrum and characteristic features have been reproduced well for both 1 st & 2 nd 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

22

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

Collective Hamiltonian 6

Collective Parameter 7

Collective Parameter 7

Collective Parameter 7