nuclear structure and dynamics within the energy density functional theory
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Nuclear Structure and dynamics within the Energy Density Functional theory. Denis Lacroix IPN Orsay. Outline:. Low lying modes and Collective excitations. Configuration mixing and spectroscopy. Some open issues in beyond mean- field approaches. - PowerPoint PPT PresentationTRANSCRIPT
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Nuclear Structure and dynamics within the Energy Density Functional theory
Denis Lacroix IPN Orsay
Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and Th. Duguet
Outline:
Low lying modes and Collective excitations
Configuration mixing and spectroscopy
Some open issues in beyond mean-field approaches
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GeneralitiesPairing effect on nuclear dynamic
2n-transfer reactions2n-break-up reactions
Assié and Lacroix, PRL102 (2009) Scamps, Lacroix, PRC 87 (2013)
Scamps, Lacroix, arXiv:1307.1909
Goal
Systematic study of the pairingInfluence on nuclear dynamics
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Pair transfer: the nuclear structure and reaction perspective
Nuclear reaction on a meshTDHF is a standard tool : Slater
Single-particle evolutionSimenel, Lacroix, Avez, arXiv:0806.2714v2
BCS limit of TDHFB (also called Canonical basis TDHFB)
Neglect
Introduction of pairing: TDHFB
Quasi-particle evolution
(Active Groups: France, US, Japan…)
TDHFB = 1000 * (TDHF)
Less demanding than TDHFB
Reasonable results for collective motion
Sometimes more predictive than TDHFB
Ebata, Nakatsukasa et al, PRC82 (2010)
Scamps, Lacroix, Bertsch, Washiyama, PRC85 (2012)
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Collective motion
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Pairing effect on nuclear collective motionComparison TDHF+BCS / QRPA
Illustration with the GQR
Strength distribution in deformed 34Mg
QRPA: C. Losa, et al PRC 81, (2010).
QRPA
TDHF+BCS
Q22Q20
Almost no difference between TDHF+BCS and TDHFB (QRPA)
Main effect of pairing is to set the deformation
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Systematic in Spherical nuclei
Isoscalar GQR Isovector GQR
263 nuclei324 nuclei
38S
Scamps, Lacroix, PRC88 (2013)
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Systematic in deformed nuclei
Scamps, Lacroix, arXiv:1401.5211
Excitation operators
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Systematic in deformed nuclei: illustration
QRPA: Yoshida, Nakatsukasa, PRC88 (2013)
Collective energy Damping width
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Systematic in deformed nuclei: fragmentation and damping
prolateoblate
Energy splitting:
Damping is more complex:
High order deformation is important
Scamps, Lacroix, arXiv:1401.5211
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Systematic in deformed nuclei: triaxial nuclei
54 triaxial nuclei
Scamps, Lacroix, arXiv:1401.5211
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Difficulties
TDHF+BCSExp
QRPA (Bertsch, Terasaki, Engel)
Low lying 2+ states
Collective motionMean-field
Collective sector
Low-lying sector
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Lacroix, Ayik, Chomaz, Prog. Part and Nucl. Phys. (2004)
Improving collective state description
Coll2 1
Standard RPA states
Coupling to ph-phonon
Coupling to 2p2h states
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Lacroix, Ayik, Chomaz, Prog. Part and Nucl. Phys. (2004)
Improving collective state description
GQR in 208PbGQR in 40Ca
EWSR
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Remaining difficulty
Perturbative treatment of the couplingColl
2 1
?
Within the EDF:
Requires better defined techniques
Requires to define power counting
No cut-offwith cut-off
Most often UV divergent
No real perturbative scheme
See for instance:
Moghrabi, Grasso, Phys. Rev. C 86 (2012)
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Improving low-lying state description
TDHF+BCSExp
QRPA
Low lying 2+ states
Prediction from TDHF+BCS:
Implementing configuration mixing
Bertsch et al, PRL99 (2007)
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74KrMean-Field
Energy
0+
0+0+
2+
2+ 2+
4+
4+
6+
8+
Corr
elati
on
Ener
gy
Single Reference (SR)-Mean-Field
Ground state
Multi- Ref. (MR)-GCMBeyond mean-field
Configuration mixing within Energy Density Functional
Restoration of broken symmetries
(particle number, angular momentum, …)
Excited state and spectroscopy
… but we are starting from a functional theory framework
Formal and practical difficulties
Yes but
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Single Reference (SR)-Mean-Field
Ground state
Multi- Ref. (MR)-GCMBeyond mean-field
Towards systematic studies with mean-fieldConfiguration mixing within Energy Density Functional
M meshpoints
Lacroix et al, PRC79 (2009), Bender et al, PRC79 (2009),Duguet et al, PRC79 (2009)
Problem due to the direct mapping Between Hamiltonian and EDF
Connected to self-interaction and self-pairing
A solution has been proposed (not for ra)
This solution does not work For most complex calculations
Before correction
Corrected
SIII force
PRELIMINARY
Angular momentum+particle number proj.
Requires to come back to true interaction?
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Difficulties
r2, r3
r2, r3 ,r4
r2, r3 ,r4 , r5
Fitting the Equation of state is not so simple
Requires at list a 4 body interaction
Fitting both mean-field and pairingWith the same interaction also not easy
Ener
gyEn
ergy
density
density
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Summary/Discussion:
Systematic of collective motion and low lying excitations
Recent progress in the development of transport model with pairing
Damping is underestimated
Low lying states are poorly described
Mean energy, … are quite nicely reproduced
Need for Beyond-Mean-field approach
Perturbative techniques
Non-perturbative techniques like GCM
Beyond Mean-field approaches within a functional theory have to be applied withspecial caution.