Post on 03-Jan-2016
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
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
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)
Collective motion
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
Systematic in Spherical nuclei
Isoscalar GQR Isovector GQR
263 nuclei324 nuclei
38S
Scamps, Lacroix, PRC88 (2013)
Systematic in deformed nuclei
Scamps, Lacroix, arXiv:1401.5211
Excitation operators
Systematic in deformed nuclei: illustration
QRPA: Yoshida, Nakatsukasa, PRC88 (2013)
Collective energy Damping width
Systematic in deformed nuclei: fragmentation and damping
prolateoblate
Energy splitting:
Damping is more complex:
High order deformation is important
Scamps, Lacroix, arXiv:1401.5211
Systematic in deformed nuclei: triaxial nuclei
54 triaxial nuclei
Scamps, Lacroix, arXiv:1401.5211
Difficulties
TDHF+BCSExp
QRPA (Bertsch, Terasaki, Engel)
Low lying 2+ states
Collective motionMean-field
Collective sector
Low-lying sector
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
Lacroix, Ayik, Chomaz, Prog. Part and Nucl. Phys. (2004)
Improving collective state description
GQR in 208PbGQR in 40Ca
EWSR
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)
Improving low-lying state description
TDHF+BCSExp
QRPA
Low lying 2+ states
Prediction from TDHF+BCS:
Implementing configuration mixing
Bertsch et al, PRL99 (2007)
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
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?
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
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.