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Giant and Pygmy Resonance in Relativistic Approach

Giant and Pygmy Resonance in Relativistic Approach. The Sixth China-Japan Joint Nuclear Physics May 16-20, 2006 Shanghai Zhongyu Ma China Institute of Atomic Energy, Beijing Collaborators: Ligang Cao, Baoqiu Chen, Jun Liang. Introduction.

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Giant and Pygmy Resonance in Relativistic Approach

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  1. Giant and Pygmy Resonance in Relativistic Approach The Sixth China-Japan Joint Nuclear Physics May 16-20, 2006 Shanghai Zhongyu Ma China Institute of Atomic Energy, Beijing Collaborators:Ligang Cao, Baoqiu Chen, Jun Liang

  2. Introduction Nucleus moving away from the valley of -stability diffuse neutron: neutron skin, hallo structure, new magic numbers, new modes of excitations, etc. Significant interest on low-energy excited states GDR (Coulomb excitations) restoring force proportional to the symmetry energy Pygmy resonance Loosely bound neutron coherently oscillate against the p-n core neutron density distribution, neutron radius, skin et al. density dependence of symmetry energy Astrophysical implications

  3. Fully Consistent RRPA RRPA -- Consistent in sense: ph residual interaction determined from the same Lagrangian for g.s. RRPA polarization operator i=,, i=1, , 3 for , , , respectively consistent to RMFno sea approx. Include both ph pairs and h pairs Z. Y. Ma, et al., Nucl. Phys. A703(2002)222 RRPA TDRMF at small amplitude limit TDRMF at each time no sea approximation  is calculated in a stable complete set basis P.Ring et al., Nucl. Phys. A694(2001)249

  4. Z.Y. Ma, et al., Nucl. Phys. A686(2001)173 Fig: ISGMR NL1,NL3,TM1,NLSH M.E. of vector fields coupling h and ph----Largely reduced due to Dirac str. Cancellation of the  &  fields --- not take place, Large M.E. coupling h and ph exist

  5. Treatment of the continuum  Resonant states in the continuum Metastable states in the centrifugal & Coulomb Barrier Discretization of the continuum Expansion on Harmonic Oscillator basis Box approximation: set a wall at a large distance Exact treatment of the continuum Set up a proper boundary condition Single particle resonance with energy and width Green’s function method Scattering phase shift Centrifugal & Coulomb Total Nuclear Pot.

  6. Scattering phase shift Boundary conditions: Normalized by phase shift:  = /2 resonant state For proton, Dirac Coulomb functions have to be solved for  ~1 Z large large diff. from norn Coulomb wf Cao & Ma PRC66(02)024311 W. Grainer “Rel. Quantum Mach.”

  7. Example of resonance states More resonant states for p than those for n due to the Coulomb barrier

  8. Resonant continuum in pairing correlations Pairing correlationsplay a crucial role in MF models for open shell HF+BCS and RMF+BCS simple successful in nuclei when F not close to the continuum HFB and RHB important innuclei near the drip-line HF eq. + gap eq. are solved simultaneously states in continuum are discretized in both methods Resonant states : HFB eq. are solved with exact boundary conditions Grasso, Sandulescu, Nguyen, PRC64(2001)064321 Discretization of the continuum overestimates pairing corr. Effect of the continuum on pairing --- mainly by a few resonant states in the continuum RMF+BCS with resonant states including widths

  9. BCS with the continuum Gap equation : Continuum level density Nucleon densities:

  10. Pairing correlation energy BCS are good in the vicinity of the stable line. Width effects are large for nuclei far from the stability line. Cao, Ma , Eur. Phys. J. A 22 (2004)189

  11. Quasi-particle RRPA Response function Unperturbed polarization operator BCS occupation prob. Outside the pairing active space Positive unoccu. states occu. states Negative states

  12. Ni-isotopes Extended RMF+BCS s.p. resonant states 2d5/2,2d3/2,1g7/2,2f7/2,1h11/2, G=20.5/A MeV Cao, Ma, Modern Phys. Lett. A19(2004)2845

  13. IVGDR Ni-isotopes 58Ni – 64Ni are stable vibration of p-n Ni-isotopes A=70~96 The response functions of IVGDR in QRRPA Loosely bound neutron coherently oscillate against the p-n core EH ~ 16 MeV low-lying dipole <10 MeV

  14. IVGDR in Ni-isotopes GDR restoring force proportional to the symmetry energy Linear dep. on the neutron skin Cao, Ma, Modern Phys. Lett. A19(2004)2845

  15. Experiments on GDR Gibelin and Beaumel (Orsay), exp. at RIKEN inelastic scattering of26Ne + 208Pb 60 MeV/u 26Ne secondary beam Dominated by Coulomb excitations selective for E1 transitions. Thesis of J. Gibelin IPNO-T-05-11 Future work: 28Ne + 208Pb Theoretical investigation – practical significance Cao, Ma, PRC71(05)034305

  16. Properties of 26,28Ne Extended RMF+BCS with NL3 GQR check the validity of spherical assumption

  17. 26Ne, 28Ne IVGDR Cao, Ma, PRC71(05)034305

  18. Sum rule Low-lying GDR in 26Ne exhaust about 4.9% of TRK sum rule 28Ne 5.8%

  19. Comparisons of Low-lying dipole state in 26Ne Authors Methods Shape Result Elias(Orsay) SHF+BCS+ spherical 11.7 not coll. QRPA(RF) Cao, Ma(CIAE) RMF+BCS(R.) spherical 8.4(5%) coll. PRC71(2005)034305 +QRRPA(RF) Peru(CEA) def. HFB(Gogny) Spherical 10.7 coll. +QRPA(Matrix) Ring(TUM) def. RHB +QRRPA Deformed 7.9 9.3 less coll. (Matrix) Exp.(Gibelin,Beaumel) measure ? ~9(5%) IPNO-T-05-11 Preliminary

  20. Symmetry Energy and GDR Restoring force of GDR Symmetry energy in NM All parameters give very good description of g.s. properties, NM saturations Centroid energy of GDR Ecen=m1/m0 Linear dep on the symmetry energy at saturation energy May give constraint: 33 MeV< asym(0)<37 MeV

  21. Density dep. of symmetry energy Non linear- coupling Todd, Pickarewicz, PRC67(03) Modify the poorly known density dep. of symmetry energy Without changing the agreement with existing NM, g.s. properties Softening of the symmetry energy NL3 B/A=16.24MeV asym=37.3 MeV 0=.148fm-3(kF=1.3fm-1) K=272 MeV asym=25.67 MeV at =.1fm-3(kF=1.15fm-1)

  22. Ground state properties in 132Sn B/A, rp slightly changed asym softened rn-rpbecomes small

  23. Pygmy Resonance & Symmetry Energy GSI Epeak(Pygmy)=8.0 MeV above one n separation energy Epeak(GDR)= 13.8, 14.0, 14.2 MeV Adrich et al. PRL95(05)132501 GDR : peak energy is shifted dep. on the symmetry energy at 0 Pygmy resonance is kept unchanged at 8.0 MeV It may set up a constraint on the density dep. of symmetry energy

  24. Summary  Theoretical investigations on Pygmy resonance in quasi-particle RPA non-relativistic QRPA relativistic approaches QRRPA  Pairing correlation is important, coupling to the continuum Extended RMF+BCS the s.p. resonance in the continuum including widths  GDR -- restoring force is proportional to the symmetry energy systematic study 33 MeV < asym(0) < 37 MeV  New excitation modes in exotic nuclei Pygmy modes are related to neutron skin and density dependence of symmetry energy

  25. Thanks

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