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Role of deformation on giant resonances within the QRPA and the Gogny force

Role of deformation on giant resonances within the QRPA and the Gogny force. S.P É RU. Formalism. HFB+QRPA. { b + b} quasi-particle (qp) creation and annihilation operators. In sph erical symmetry , QRPA states { q + } are obtained for each block J  .

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Role of deformation on giant resonances within the QRPA and the Gogny force

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  1. Role of deformation on giant resonances within the QRPA and the Gogny force S.PÉRU

  2. Formalism HFB+QRPA {b+b}quasi-particle (qp) creation and annihilation operators. In sphericalsymmetry, QRPA states{q+} are obtained for each block J. In axial symmetry , they are obtained for each block K. Kp≤Jp QRPA states are solutions of In our approach, The effective interactionD1Sis used both in the HFB mean field and in the QRPA matrix.

  3. Restoration of rotational symmetry for deformed states We want to calculate: for all QRPA states (K ≤ J) For example: Jπ = 2+ In intrinsic frame Using rotational approximation and relations for 3j symbols Using time reversal symmetry, three independent calculations (Kπ = 0+, 1+, 2+) are needed.

  4. Role of deformation on giant resonances within the QRPA and the Gogny force, SP and H. Goutte, PRC 77, 044313 (2008) Potential Energy Surfaces

  5. Pairing Energies

  6. IV Dipole

  7. IsoVector Giant Dipole resonance Systematic law: EIVGDR 31.2 A-1/3 3 + 20.6 A-1/6 MeV

  8. Monopole D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999) 014304 D.H. Youngblood, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65,(2002) 034302 0 10 20 30 40 MeV 0 10 20 30 40 MeV

  9. Monopole

  10. Giant Monopole resonance Systematic law : EGMR = 80 A-1/3 MeV

  11. Quadrupole D.H. Youngblood, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65, (2002) 034302 D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999)014304 0 10 20 30 40 MeV

  12. Quadrupole

  13. Giant Quadrupole resonance Systematic law: EGQR = 63 A-1/3 MeV

  14. Octupole

  15. Theoretical Octupole resonances Systematic law ELEOR= 30 A-1/3 MeV Systematic law For heavy nuclei EHEOR= 110 A-1/3 MeV

  16. J.Gibelin, Ph D Thesis Orsay 2005 ORSAY-RIKEN collaboration  31.2 A-1/3 + 20.6 A-1/6 Theoretical Predictions in Neons Systematic, E1 Strength predicted by QRRPA calculations 1.2 S [e2fm2/MeV] 28Ne 0 26Ne 0 24Ne 0 22Ne 0 20Ne 0 Cao L.-G. and Ma Z.-Y. Phys. Rev. C 71, 034305 (2005) E* [MeV]

  17. Lead 30 Pb Target S1n S2n ▬▬ L=1 background subtracted ▬▬ L≥2 20 3.3 ▬▬ SUM 10 2.0 1.7 0 background subtracted GS 25Ne [MeV] GS 26Ne θCM [degree] 0 4 6 8 10 12 16 20 E* [MeV] J.Gibelin, Ph D Thesis Orsay 2005 ORSAY-RIKEN collaboration L=1 L=2 Sum B(E1)  = 0.49 ± 0.16 e2 fm2 %STRK = 4.9 ± 1.6 @ 9 MeV J. Gibelin et al, PRL 101, 212503 (2008)

  18. responses for 26 Ne IV Dipole M1/M0=23.13 MeV Quadrupole Monopole M1/M0=20.73 MeV M1/M0=19.75 MeV 63 A-1/3 = 21.26 MeV

  19. Transition densities for pygmy 26Ne Core is not inert

  20. Main components in pygmy wave function Proton 2qp components 15.97 MeV 2s1/2 1p1/2 17.60 MeV 1d5/2 1p3/2 17.48 MeV 1d5/2 1f7/2 Neutron 2qp components 10.52 MeV “2p3/2” 2s1/2 13.68 MeV “1f7/2” 1d5/2 12.43 MeV “2p1/2” 2s1/2 10.82 MeV “2p3/2” 1d5/2 18.50 MeV 1d3/2 1p1/2 Neutron

  21. responses for 26 Ne IV Dipole M1/M0=23.13 MeV Quadrupole Monopole M1/M0=20.73 MeV M1/M0=19.75 MeV 63 A-1/3 = 21.26 MeV

  22. E(2+) (MeV) théo. expt. B(E2;0+2+) (e2fm4) 0 b Z 8 10 12 14 16 18 HFB+GCM with Gogny force D1S 26Ne is found to be deformed : <b>=0.3, <g>=30° A. Obertelli, SP, J.-P. Delaroche, A. Gillibert, M. Girod et H. Goutte, Phys. Rev. C 71, 024304 (2005) J. Gibelin et al, PRC 75, 057306 (2007) QRPA

  23. CONCLUSION A fully consistent microscopic axially-symmetric-deformed (ASD) QRPA approach using the D1S Gogny force as been applied to light even-even Mg and Si isotopes. In deformed nuclei IVGDR is found split into 2 major components K=0 and |K|=1. In prolate nuclei K=0 components are found in the low energy part of the spectra, and |K|=1 in oblate ones. Isoscalar monopole resonances also display a splitting in deformed nuclei. Isoscalar quadrupole and octupole resonances are found to be well fragmented in particular in well-deformed nuclei. Results obtained in 24Mg and in 28Si show that the Gogny interaction qualitatively reproduces known resonances without resorting to any readjustment of parameters. Good agreement between experimental and QRPA results And coherence with GCM+GOA calculations using the same interaction (26Ne and Ni isotopes)

  24. Test of QRPA wave functions in proton inelastic scattering… Perspectives 36S HFB+GCM+GOA E (2+1) = 2.34 MeV B(E2) = 375 e2fm4 HFB+QRPA E (2+1) = 3.29 MeV B(E2) = 139.7 e2fm4 Exp E (2+1) = 3.29 MeV B(E2) = 100 e2fm4 E. Bauge and S. Péru

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