SomeresultsobtainedwithGognyforce includedinHFB ...fustipen.ganil.fr/conferences/2015/workshops/new-directions-for... · SomeresultsobtainedwithGognyforce includedinHFB,QRPAaswellasin

FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru

Some results obtained with Gogny forceincluded in HFB, QRPA as well as in

configuration mixing GCM like approach

Sophie Péru

M. Dupuis, S. Hilaire, F. Lechaftois (CEA, DAM), M. Martini (Ghent University, Belgium),

S. Goriely (Université Libre de Bruxelles, Belgium),I. Deloncle (CSNSM, Orsay)


Static mean field (HFB) for Ground State Properties :• Masses• Deformation• (Single particle levels) Beyond static mean field approximation (5DCH or QRPA)

for description of Excited State Properties• Low-energy collective levels • Giant Resonances

Amedee database : http://www-phynu.cea.fr/HFB-Gogny_eng.htmS. Hilaire & M. Girod, EPJ A33 (2007) 237

Gogny

Short Reminder


Beyond mean field … with 5DCH

(2 vibr. + 3 rot.) = 5 Dimension Collective Hamiltonian

( ) ( ) ( )20202 and 0nm,

12/12/123

1

22

,,2

ˆ

2ˆ aaVaaV

aBD

aD

J

IH

nmn

mk k

kcoll ∆−+

∂∂

∂∂−= ∑∑

=

−−

=

hh

Potential energy surfaces

axial TriaxialWave functionof the collective 01

+


D1S: J. P. Delaroche et al. PRC 81, 014303 (2010)D1M: S. Hilaire et al. PRC 86, 064317 (2012)

Some exploitation of 5DCH with Gogny forces

S. Goriely, S. Hilaire, M. Girod, S. Péru , PRL 102, 242501 (2009)

Systematics studies


N=20, 32Mg

E E E E (2(2(2(2++++1111) ) ) ) Theo.Theo.Theo.Theo. = 1.32 MeV= 1.32 MeV= 1.32 MeV= 1.32 MeV

E E E E (2(2(2(2++++1111) ) ) ) ExpExpExpExp.... = 885 = 885 = 885 = 885 keVkeVkeVkeV

N=28, 44S

EEEE(2(2(2(2++++1111))))Theo. = 1.46 MeV, = 1.46 MeV, = 1.46 MeV, = 1.46 MeV,

EEEE(2(2(2(2++++1111) ) ) ) Exp. = 1.297 = 1.297 = 1.297 = 1.297 ((((0.0180.0180.0180.018))))MeV,MeV,MeV,MeV,

BBBB((((EEEE2222,0,0,0,0++++gsgsgsgs→→→→2222++++

1111)))) = 420 e= 420 e= 420 e= 420 e2222fmfmfmfm4 4 4 4

BBBB((((EEEE2222,0,0,0,0++++gsgsgsgs→→→→2222++++

1111)))) = 314 = 314 = 314 = 314 ((((88888888)))) eeee2222fmfmfmfm4444S. Péru, M. Girod, JF. Berger , Eur. Phys. J. A 9,35-47, (2000)

Shell closure studies with 5DCH


Further analysis : moments of inertia

32Mg


Further analysis : moments of inertia

32323232MgMgMgMg

Sulfur isotopes


N=16 5DCH

A. Obertelli, S. Péru, J.-P. Delaroche, A. Gilliber t, M. Girod et H. Goutte, Phys. Rev. C 71, 024304 ( 2005)


J. Gibelin et al, PRC 75, 057306 (2007)


0.5

1.5

2.5

E (

MeV

) Expt

D1S, 5DCH

22 24 26 28 30 32 34 36 38 40 42Z

B(E

2)

(e fm

)2

4

(a)

(b)

0.5

1.5

32.5x10

Z22 24 26 28 30 32 34 36 38 40 42

) 1+)/

E(2

1+E

(4

1.5

2

2.5

3

Expt

D1S, 5DCH

vibrator

rotor

softγ

Z22 24 26 28 30 32 34 36 38 40 42

E (

MeV

)

1

2

3

4

5 2+ 5DCH2

1+ 5DCH3

2+ 5DCH4

1+ 5DCH5

2+ 5DCH6

2+ Expt

2

1+ Expt

3

2+ Expt

4

1+ Expt

5

2+ Expt

6

Z22 24 26 28 30 32 34 36 38 40 42

(eb

)s

Q

-1

-0.5

0

(Expt)1+2

Q

(5DCH)1+2

Q

(5DCH)1+

4Q

(5DCH)1+6

Q

Z22 24 26 28 30 32 34 36 38 40 42

E (

MeV

)0.5

1

1.5

2

Expt

D1S, 5DCH

N=40

First excited 0+

L. Gaudefroy et al, Phys.Rev. C 80, 064313, (2009)



(Q)RPA approaches describe all multipolarities and all parities,collective states and individual ones, low energy and high energy states with the same accuracy.

But small amplitude approximationi.e. « harmonic » nuclei

δE/δq=0 δ2E/δq2>0

E

Beyond static mean field … with 5DCH or QRPA

5 Dimension Collective Hamiltoniandescribes ground state and excited stateswithin configuration mixing :quadrupole vibrationand rotational degrees of freedom.

Exp.

SM

5DCH

HFB+D1S

D. Sohler et al, PRC 66, 054302 (2002)S.Péru and M. Martini, EPJA (2014) 50: 88.


5DCH : A. Obertelli, et al, Phys. Rev. C 71, 024304 (2005)

HFB+QRPA versus HFB+5DCH with the same interaction

N=16 isotones

Sn isotopes (Z=50)

S.Péru and M. Martini, EPJA (2014) 50: 88.


HFB+QRPA versus HFB+5DCH with the same interaction

S.Péru and M. Martini, EPJA (2014) 50: 88.

Ni isotopes (Z=28)

Two shell (N= 28, 50) and one sub-shell (N=40) closures

! For deformed nuclei the first 2+ state is rotational

78Ni is predicted doubly magic


RPA approaches describe RPA approaches describe RPA approaches describe RPA approaches describe allallallall multipolartiesmultipolartiesmultipolartiesmultipolarties and and and and allallallall parities,parities,parities,parities,

collectivecollectivecollectivecollective states and states and states and states and individualindividualindividualindividual ones, ones, ones, ones, low energylow energylow energylow energy and and and and high energyhigh energyhigh energyhigh energy states states states states

with the same accuracy.with the same accuracy.with the same accuracy.with the same accuracy.

Within the Within the Within the Within the small amplitude approximationsmall amplitude approximationsmall amplitude approximationsmall amplitude approximation, i.e. « harmonic » nuclei, i.e. « harmonic » nuclei, i.e. « harmonic » nuclei, i.e. « harmonic » nuclei

δE/δq=0δ2E/δq2>0

E

S. Péru, H. Goutte, Phys. Rev. C 77, 044313, (2008)M. Martini, S. Péru and M. Dupuis, Phys. Rev. C 83, 034309 (2011)S. Péru et al, Phys. Rev. C 83, 014314 (2011)

Axially symetric deformed QRPA with Gogny force

Spherical RPA with Gogny force

J. Dechargé and L.Sips, Nucl. Phys. A 407,1 (1983)J.P. Blaizot, J.F. Berger, J. Dechargé, M. Girod, Nucl. Phys. A 591, 435 (1995)S. Péru, JF. Berger, PF. Bortignon, Eur. Phys. J. A 26, 25-32, (2005)

Beyond mean field… with QRPA

RPA RPA RPA RPA approaches are well adapted for describing giant resonancesapproaches are well adapted for describing giant resonancesapproaches are well adapted for describing giant resonancesapproaches are well adapted for describing giant resonances


QRPA Formalism

Particle-hole excitations

ijijjij

iij YXQ ηηηη ννν +

++=

+∑

2 quasi-particle excitations

2 p1/22 p1/22 p1/22 p1/22 p3/22 p3/22 p3/22 p3/2 1 f7/21 f7/21 f7/21 f7/2

1 d3/21 d3/21 d3/21 d3/2

2 s1/2 Fermi2 s1/2 Fermi2 s1/2 Fermi2 s1/2 Fermi1 d5/21 d5/21 d5/21 d5/2

1 p1/21 p1/21 p1/21 p1/2

1 p3/21 p3/21 p3/21 p3/2

1 s1/21 s1/21 s1/21 s1/2

26Ne

Neutron’s HFlevels

Same interaction (Gogny) in HFB and QRPA

pppp----hhhh

pppp----pppp

αα

αααη avau iii ∑ −=+ +

Hartree-Fock Bogoliubov: ε, u, v

QRPA: ω, X, Y

Ground state properties

Excited states properties

hhhh----hhhh

phphhph

pph aaYaaXQ +++=+∑

ννν

RPA QRPA


Approach limited to Spherical nuclei with no pairingApproach limited to Spherical nuclei with no pairingApproach limited to Spherical nuclei with no pairingApproach limited to Spherical nuclei with no pairing

Giant resonances in exotic nuclei:Giant resonances in exotic nuclei:Giant resonances in exotic nuclei:Giant resonances in exotic nuclei:

100Sn, 132Sn, 78Ni; S. Péru, J.F. Berger, and P.F. Bortignon, Eur. Phys. Jour. A 26262626, 25-32 (2005)

RPA in spherical symmetry

SuchSuchSuchSuch studystudystudystudy havehavehavehave shownshownshownshownthethethethe rolerolerolerole ofofofof thethethethe consistenceconsistenceconsistenceconsistencebetweenbetweenbetweenbetween meanmeanmeanmean fieldfieldfieldfield andandandand RPARPARPARPA matrixmatrixmatrixmatrix....

DipoleMonopole Quadrupole


Axially-symmetric deformed QRPA

Main features:Main features:Main features:Main features:• Possibility to treat axially-symmetric deformed nucleideformed nucleideformed nucleideformed nuclei• Pairing correlations Pairing correlations Pairing correlations Pairing correlations consistently included• Use of an unique nuclear forceunique nuclear forceunique nuclear forceunique nuclear force: finite range Gogny force- same interaction for all the nuclei- same interaction for ground state and excited states (self-consistency) essential features to treat consistently isotopic chains from drip line to drip lineessential features to treat consistently isotopic chains from drip line to drip lineessential features to treat consistently isotopic chains from drip line to drip lineessential features to treat consistently isotopic chains from drip line to drip line

J

K

( ) ( ) ( ) ( ) ( ) ( ) KJ

KMKJ

KJMK DDd

JKJM θθπ

ΩΩ−+ΩΩΩ+= −−

∫ RR4

12

to calculate: ( )KJMQλµˆ0

~for all QRPA states (K ≤ J)

For example: Jπ

= 2+

In intrinsic frameλυυ

λµυλµ YrDYr 22 ∑=

We use rotational approximation and relations for 3j symbols

( ) 2,221,120,2020

ˆ05

3ˆ05

3ˆ05

1ˆ0~

±±− ++= KKKKKK QQQKJMQ δθδθδθ

Using time reversal symmetry, three independent calculations (Kπ = 0+, 1+, 2+) are needed.

Restoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed statesRestoration of rotational symmetry for deformed states

( )λµλ

λµ YrQ ∑∝ˆ


S. Péru and H. Goutte, Phys. Rev. C 77, 044313 (2008).

0.1

0.2

0.3

0.4

K = 0-

K = 1-

26Sidipole

0 10 20 30 40 MeV

0.1

0.2

0.3

0.4 24Mg

0 10 20 30 40 MeV

0.1

0.2

0.3

0.4 22Mg

0.1

0.2

0.3

0.4 28Si

0.1

0.2

0.3

0.4 30Si

0 10 20 30 40 MeV

0.1

0.2

0.3

0.4 26Mg

0 10 20 30 40 MeV

0.1

0.2

0.3

0.4 28Mg

IV DipoleIV Dipole

QRPA in axial symmetry

PotentialEnergy

Surfaces

PotentialEnergy

Surfaces

Kπ=0- Kπ=1-

J

K

K=0

K=1


Dipole response for Neon isotopes

20Ne 22Ne

24Ne 26Ne 28Ne

18Ne

Increasing neutron number•Low energy dipole resonances and shift to low energies•Increasing of fragmentation 26Ne : B(E1) = 0.49 ± 0.16 e 2 fm 2 %STRK = 4.9 ± 1.6 @ 9 MeV

J. Gibelin et al, PRL 101, 212503 (2008)

B(E1)=0.173 e2fm 2

@ 10.69 MeV


M. Martini, S. Péru and M. Dupuis, Phys. Rev. C 83, 034309 (2011)

Dipole response for Neon isotopes and N=16 isotones

Increasing |N-Z| number :•Low energy dipole resonances shift to low energies•Increasing of fragmentation and collectivity

PD

RG

DR


Multipolar responses for 238U

J

K

Heavy deformed nucleus massively parallel computation

S. Péru et al, PRC 83, 014314 (2011)

0+ 1-

2+ 3-


(n, x n) cross section on 238UProblem of underestimation of

n emission cross section at high energy

QRPA QRPA QRPA QRPA providesprovidesprovidesprovidesenoughenoughenoughenough collective collective collective collective contributioncontributioncontributioncontribution

M. Dupuis, S.Péru, E. Bauge and T. Kawano,13th International Conference on Nuclear Reaction Mechanisms, Varenna 2012CERN-Proceedings-2012-002, p 95

Beyond the nuclear structure


Nuclear Masses

Comparison with experimental data (2149 nuclei: Audi, Wapstra & Thibault 2003)

r.m.s = 0.798 MeV

S. Goriely, S. Hilaire, M. Girod, S. Péru , PRL 102, 242501 (2009)

Gogny D1M


We calculate E1 strength for all the nuclei for which photoabsorption data exist

Dipole excitations in QRPA and photoabsorption results

Spherical nuclei First peak Second peak

Deformed nuclei

D1S versus D1M


We calculate E1 strength for all the nuclei for which photoabsorption data exist


Spherical nuclei First peak Second peak

Deformed nuclei

Size of the basis


With folding and shift ….

Dipole excitations in QRPA and photoabsorption results σ[m

b]

28Si

Exp.

QRPA

60Ni 70Ge 74Ge 76Ge 80Se

90Zr 94Zr 94Mo 98Mo 116Sn 120Sn

124Te 128Te 138Ba 142Ce 144Nd 148Nd

144Sm 150Sm 158Gd 174Yb 206Pb 232Th


To take into account complex configurations as well as coupling with phonons, the deformed QRPA strength SE1(w) is folded with a Lorentzian function.

The width of the Lorentzian is adjusted on experimental data (RIPL-3 IAEA) while the energy shift is related to the number of 4qp keeping in this way a connection with our microscopic calculation.

S .Goriely, M. Martini, S. Hilaire, F. Lechaftois and S. Péru

Calculations performed also for isotopic chains of astrophysical interest (e.g. Sn).



γ- ray strength functions predictions for exotic nuclei

e.g. Sn isotopes


Photoneutron cross sections for Mo isotopes


Photoabsorption cross sections for Mo isotopes


Dipole electric and magnetic excitations for Zr isotopes

E1

H. Utsunomiya et al, PRL 100, 162502 (2008)

M1

E1

M1H. Utsunomiya et al. (2008)


p n

p n

(N,Z)

(N-1,Z+1)

(N,Z)

(N-1,Z+1)

(N,Z)

(N-1,Z+1)

(N,Z)

p

n

p

p

n

n

(N,Z)(N,Z)

e-e-

e-

e-

ν

ν

γγγγ γγγγ

W+ W+ π+

π0or

Charge exchange:Charge exchange:Charge exchange:Charge exchange:

Photo-absorption Electron scattering (p,p) or (n,n)

β decay Neutrino scattering (p,n) or (3He,t)

Nuclear Excitations

Spin-isospin nuclear excitations (in particular GT) • Crucial role in nuclear physics, astrophysics and particle physics• Experimentally studied via charge exchange reactions , e.g. (p,n) and β decay• Theoretical models to study the nuclei experimentally inaccessible


pnQRPA

General expression

QRPA

pnQRPA

pppp nnnn

pppp nnnn


Main charge exchange excitations

IsobaricIsobaricIsobaricIsobaric AnalogAnalogAnalogAnalog ResonanceResonanceResonanceResonance (IAR)(IAR)(IAR)(IAR)

Gamow Teller (GT)Gamow Teller (GT)Gamow Teller (GT)Gamow Teller (GT)

pppp nnnn

pppp nnnn

isospin flip τspin flip σ

S=0

S=1

T=1

T=1

Jπ=0+

Jπ=1+

pppp nnnn

isospin flip τ


F: 13.9999993456112 GT/3: 13.9999993456064

F: 32.0000000000001 GT/3: 32.0000000000001

114Sn132Sn

Ikeda

Checks

Fermi

When Coulomb repulsion is out of HFB calculations, the energy of the IAR dives to zero.

Sum Rules :


Gogny pnQRPA Strength Distributions

M. Martini, S. Péru and S. Goriely, Phys. Rev. C 89, 044306 (2014)

Good agreement with experimental data


An example of deformed nucleus : 76Ge

prolate

HFBHFBHFBHFBD1M D1M D1M D1M

2

GT Jπ=1+ distributions obtained by adding twice the Kπ=1+ result to the Kπ=0+ one

• The deformation tends to increase the fragmentation• Displacements of the peaks • Deformation influences the low energy strength hence β decay half-lives are expected to be affected

Experiment Thies et al., Phys. Rev. C 86, 014304 (2012)

pnQRPA-D1M

β2(min. HFB) = 0.15 γ(min.HFB) = 0°

β2 (0+1:5DCH) = 0.26 γ(0+

1:5DCH) = 26°


β- decay half-life T1/2

Comparison Comparison Comparison Comparison with experimental data for with experimental data for with experimental data for with experimental data for 145 even145 even145 even145 even----even nuclei even nuclei even nuclei even nuclei

• Deviation with respect to data rarely exceeds one order of magnitude• Larger deviations for nuclei close to the valley of β-stability, as found in most models

G.Audi et al. Chinese Phys. C 36363636,

1157 (2012)


Our model Other models

GT2:GT2:GT2:GT2:Tachibana et al. Prog. Theor. Phys., 84, 641 (1990)

FRDM:FRDM:FRDM:FRDM: Moller et al., ADNDT, 66,131 (1997)

Comparison with other models


β- decay half-lives of deformed isotopic chains


β- decay half-lives of the N=82, 126, 184 isotones

Relevance for the r-process nucleosynthesis

Shell Model : MartinezShell Model : MartinezShell Model : MartinezShell Model : Martinez----PinedoPinedoPinedoPinedo et al., PRL 83, 4502 (1999) et al., PRL 83, 4502 (1999) et al., PRL 83, 4502 (1999) et al., PRL 83, 4502 (1999) DF3+cQRPA : DF3+cQRPA : DF3+cQRPA : DF3+cQRPA : BorzovBorzovBorzovBorzov et al., PRC 62, 035501 (2000)et al., PRC 62, 035501 (2000)et al., PRC 62, 035501 (2000)et al., PRC 62, 035501 (2000)


Even and oddoddoddodd systems, deformed and spherical nuclei

28

Preliminary results

Recent experimental resultsZ.Y. Xu et al, PRL 113, 032505 (2014)β-decay Half lives of 76,77Co, 79,80Ni and 81Cu :Experimental indication of a Doubly Magic 78Ni

Extension to odd systems in collaboration with

Isabelle Deloncle (CSNSM) Orsay


To summarize

Great successes using the finite range Gogny force:

5DCH : good reproduction of collective low energy spectra and shell effectsQRPA : good description of pygmy and giant resonances in spherical or deformed nuclei

QRPA and 5DCH complete each other.

Some results were shown:

* Self-consistent QRPA approach has been applied to the deformed nuclei up to 238U.

* IsoScalar-IsoVector mixing for low-lying dipole states in Ne isotopes and N=16 isotones.

* QRPA results successfully used in reaction models : (n, x n) , photoabsorption …

Extension of QRPA to charge exchange : Extension of QRPA to charge exchange : Extension of QRPA to charge exchange : Extension of QRPA to charge exchange :

* For magic spherical nuclei, IAR and GT results in good agreement with data.* The role of the intrinsic deformation has been shown for prolate 76Ge.* Predictions of the β decay half-life time are compatible with experimental data.

* Satisfactory agreement with experimental half-lives which justifies the additional study on the exotic neutron-rich N = 82, 126 and 184 isotonic chains (r-process).

Promising preliminary results for odd nuclei.

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SomeresultsobtainedwithGognyforce includedinHFB ...fustipen.ganil.fr/conferences/2015/workshops/new-directions-for... · SomeresultsobtainedwithGognyforce includedinHFB,QRPAaswellasin