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.