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Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay...

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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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Page 1: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 2: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 3: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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)

Page 4: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Collective motion

Page 5: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 6: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Systematic in Spherical nuclei

Isoscalar GQR Isovector GQR

263 nuclei324 nuclei

38S

Scamps, Lacroix, PRC88 (2013)

Page 7: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Systematic in deformed nuclei

Scamps, Lacroix, arXiv:1401.5211

Excitation operators

Page 8: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Systematic in deformed nuclei: illustration

QRPA: Yoshida, Nakatsukasa, PRC88 (2013)

Collective energy Damping width

Page 9: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Systematic in deformed nuclei: fragmentation and damping

prolateoblate

Energy splitting:

Damping is more complex:

High order deformation is important

Scamps, Lacroix, arXiv:1401.5211

Page 10: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Systematic in deformed nuclei: triaxial nuclei

54 triaxial nuclei

Scamps, Lacroix, arXiv:1401.5211

Page 11: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Difficulties

TDHF+BCSExp

QRPA (Bertsch, Terasaki, Engel)

Low lying 2+ states

Collective motionMean-field

Collective sector

Low-lying sector

Page 12: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 13: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Lacroix, Ayik, Chomaz, Prog. Part and Nucl. Phys. (2004)

Improving collective state description

GQR in 208PbGQR in 40Ca

EWSR

Page 14: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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)

Page 15: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Improving low-lying state description

TDHF+BCSExp

QRPA

Low lying 2+ states

Prediction from TDHF+BCS:

Implementing configuration mixing

Bertsch et al, PRL99 (2007)

Page 16: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 17: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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?

Page 18: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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

Page 19: Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

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.


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