QRPA with the Gogny force with or without charge exchange applied to - - PowerPoint PPT Presentation

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QRPA with the Gogny force with or without charge exchange applied to - - PowerPoint PPT Presentation

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QRPA with the Gogny force with or without charge exchange applied to spherical and deformed nuclei Sophie Pru M. Dupuis, S. Hilaire, F. Lechaftois (CEA, DAM), M. Martini (Ghent University, Belgium), S. Goriely (Universit Libre de

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COMEX5, September 2015

DAM, DIF, S. Péru

QRPA with the Gogny force with or without charge exchange applied to spherical and deformed nuclei

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)
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COMEX5, September 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.htm

  • S. Hilaire & M. Girod, EPJ A33 (2007) 237

Gogny

Short Reminder

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COMEX5, September 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-

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COMEX5, September 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

Nuclear Data Sheets 118 (2014) 273- 275

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COMEX5, September 2015

DAM, DIF, S. Péru

2 2 2 2 2 2 2

) ) ( ( 1 ) , ( E E E E L Γ + ∆ − − Γ = ω π ω fE1(E)= L(E,ω)S

E1(ω)dω −∞ +∞

∫

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

Model 0: All parameters are independent of the energy and identical for all nuclei. ∆ = 2 MeV and Г = 2.5 MeV Model 1: Г is adjusted on each photoabsortion cross section ∆ is energy dependent :Δ = Δ + Δ ω ; Δ is constant and Δ ω = × ω 30 ⁄ Model 2: Г is adjusted on each photoabsortion cross section ∆ is energy dependent :Δ = Δ + Δ ω ; Δ is constant and Δ ω = × ω ω ⁄

Semi-empirical broadening of the GDR

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COMEX5, September 2015

DAM, DIF, S. Péru

Semi-empirical broadening of the GDR 1/3

Model 0 Model 1 Model 2 Exp data

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COMEX5, September 2015

DAM, DIF, S. Péru

Model 0 Model 1 Model 2

Semi-empirical broadening of the GDR 2/3

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DAM, DIF, S. Péru

Semi-empirical broadening of the GDR 3/3

Model 0 Model 1 Model 2

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DAM, DIF, S. Péru

γ- ray strength functions predictions for exotic nuclei

Comparison with other models

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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 γ γ γ γ γ γ γ γ W- W+ π+ π0

  • r

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

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COMEX5, September 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

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DAM, DIF, S. Péru

An example of deformed nucleus : 76Ge

prolate HFB HFB HFB HFB D1M 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°

Martini, Péru, Goriely, PRC 89, 044306 (2014)

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COMEX5, September 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 even 145 even 145 even 145 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 36 36 36 36, 1157 (2012)

Martini, Péru, Goriely, PRC 89, 044306 (2014)

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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

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DAM, DIF, S. Péru

β- decay half-lives of deformed isotopic chains

Martini, Péru, Goriely, PRC 89, 044306 (2014)

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DAM, DIF, S. Péru

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

Relevance for the r-process nucleosynthesis

Shell Model : Martinez Shell Model : Martinez Shell Model : Martinez Shell Model : Martinez-

  • Pinedo

Pinedo Pinedo Pinedo 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 : Borzov Borzov Borzov Borzov et al., PRC 62, 035501 (2000) et al., PRC 62, 035501 (2000) et al., PRC 62, 035501 (2000) et al., PRC 62, 035501 (2000)

Martini, Péru, Goriely, PRC 89, 044306 (2014)

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COMEX5, September 2015

DAM, DIF, S. Péru

Even and odd

  • dd
  • dd
  • dd systems, deformed and spherical nuclei

28

Preliminary results

Recent experimental results Z.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

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DAM, DIF, S. Péru

To summarize

Great successes using the finite range Gogny force:

Self-consistent QRPA approach has been applied to the deformed nuclei up to heavy ones. The GDR energy position with QRPA is systematically predicted ~2MeV above the experimental values. Systematic studies have been undertaken for dipole response over the whole nuclear chart. 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-lives 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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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 approximation i.e. « harmonic » nuclei

δE/δq=0 δ2E/δq2>0 E

5 Dimension Collective Hamiltonian describes ground state and excited states within configuration mixing : quadrupole vibration and 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.

Some perspectives

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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.

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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

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DAM, DIF, S. Péru

According to the great successes using the finite range Gogny force:

5DCH : good reproduction of collective low energy spectra and shell effects QRPA : good description of pygmy and giant resonances in spherical or deformed nuclei QRPA and 5DCH complete each other.

We plan to use QRPA results to improve 5DCH

See next talk: Introduction of a valence space in QRPA: impact on vibrational mass parameters and spectroscopic properties by François Lechaftois