SomeresultsobtainedwithGognyforce includedinHFB...
Transcript of SomeresultsobtainedwithGognyforce includedinHFB...
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)
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
+
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Further analysis : moments of inertia
32Mg
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Further analysis : moments of inertia
32323232MgMgMgMg
Sulfur isotopes
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
N=16 5DCH
A. Obertelli, S. Péru, J.-P. Delaroche, A. Gilliber t, M. Girod et H. Goutte, Phys. Rev. C 71, 024304 ( 2005)
Shell closure studies with 5DCH
J. Gibelin et al, PRC 75, 057306 (2007)
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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)
Shell closure studies with 5DCH
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
(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.
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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.
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Multipolar responses for 238U
J
K
Heavy deformed nucleus massively parallel computation
S. Péru et al, PRC 83, 014314 (2011)
0+ 1-
2+ 3-
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
(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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
Size of the basis
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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).
Dipole excitations in QRPA and photoabsorption results
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
γ- ray strength functions predictions for exotic nuclei
e.g. Sn isotopes
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Photoneutron cross sections for Mo isotopes
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Photoabsorption cross sections for Mo isotopes
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Dipole electric and magnetic excitations for Zr isotopes
E1
H. Utsunomiya et al, PRL 100, 162502 (2008)
M1
E1
M1H. Utsunomiya et al. (2008)
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
pnQRPA
General expression
QRPA
pnQRPA
pppp nnnn
pppp nnnn
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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 :
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
Gogny pnQRPA Strength Distributions
M. Martini, S. Péru and S. Goriely, Phys. Rev. C 89, 044306 (2014)
Good agreement with experimental data
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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°
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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)
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
β- decay half-lives of deformed isotopic chains
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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)
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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
FUSTIPEN, 16th-20th March 2015 DAM, DIF, S. Péru
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.