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