Nuclear Low-lying Spectrum and Quantum Phase Transition

Zhipan Li School of Physical Science and Technology

Southwest University

17th Nuclear Physics Workshop, Kazimierz Dolny, Poland

www.swu.edu.cn

Outline

Introduction 1

Theoretical framework2

Results and discussion3

Summary and outlook4

Quantum Phase Transition in finite system 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.

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

SphericalSpherical

DeformedDeformed

E CriticalCritical

β

Potential

Order par.

Potential

Order par.

F. Iachello, PRL2004

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

Covariant Energy Density Functional (CEDF) Covariant Energy Density Functional (CEDF)

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

Ring1996, Vretenar2005, Meng2006Ring1996, Vretenar2005, Meng2006

PES

AMP+GCM: Niksic2006, Yao2010

5D Collective Hamiltonian based on CEDF

Brief Review of the model Brief Review of the model

Coll. Potential

Moments of inertia

Mass parameters

Diagonalize:

Nuclear spectroscopy

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

Prochniak & Rohozinski, JPG36, 123101 (09)Prochniak & Rohozinski, JPG36, 123101 (09)

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)]

Microscopic Analysis of nuclear QPTMicroscopic Analysis of nuclear QPTMicroscopic Analysis of nuclear QPTMicroscopic Analysis of nuclear QPT

Potential Energy Surfaces (PESs)

Discontinuity

First order QPT First order QPT

Potential Energy Surfaces (PESs)

along β along γ

First order QPT First order QPT

Spectrum

detailed spectroscopy has been reproduced well !!

First order QPT First order QPT

Spectrum

Characteristic features:

Sharp increase of R42=E(41)/E(21) and B(E2; 21→01) in the yrast band

X(5)

First order QPT First order QPT

Single-particle levels

First order QPT First order QPT

150Nd

Microscopic analysis of Order parameters Microscopic analysis of Order parameters

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

F. Iachello, PRL2004

based on IBM

F. Iachello, PRL2004

based on IBM

1. Isotope shift & isomer shift

2. Sharp peak at N~90 in (a)

3. Abrupt decrease; change sign in (b)

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.

Microscopic analysis of Order parameters Microscopic analysis of Order parameters

Second order QPT 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, PRL2000F. Iachello, PRL2000

Second order QPT Second order QPT

PESs of Ba isotopes

Second order QPT Second order QPT

PESs of Xe isotopes

Second order QPT Second order QPT

Evolution of shape fluctuation: Δβ/ 〈 β 〉 , Δγ/ 〈 γ 〉

Second order QPT 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

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

22

Summary and outlookSummary and outlookSummary and outlookSummary and outlook

J. Meng & JCNP group

D. Vretenar & T. Niksic

P. Ring

L. Prochniak

G. A. Lalazissis

6

Collective Hamiltonian Collective Hamiltonian

7

Collective Parameter Collective Parameter

7

Collective Parameter Collective Parameter

7

Collective Parameter Collective Parameter