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Collective modes of excitation in deformed neutron-rich nuclei

@Saclay 18-20 May, 2009. Collective modes of excitation in deformed neutron-rich nuclei. Kenichi Yoshida. Contents. Uniqueness in deformed neutron-rich nuclei Deformed HFB+QRPA Collective modes in neutron-rich Mg isotopes beyond N=20

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Collective modes of excitation in deformed neutron-rich nuclei

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  1. @Saclay 18-20 May, 2009 Collective modes of excitation in deformed neutron-rich nuclei Kenichi Yoshida

  2. Contents • Uniqueness in deformed neutron-rich nuclei • Deformed HFB+QRPA • Collective modes in neutron-rich Mg isotopes beyond N=20 • Collectivity in nuclei at around the island of inversion • Summary and perspectives

  3. Uniqueness in neutron-rich nuclei Weak binding Continuum coupling Shallow Fermi level • Spatially extended structure of the single-(quasi)particle wave functions Neutron skins and halos • New shell structures • Appearance of new magic numbers/disappearance of traditional magic numbers New regions of deformation

  4. Neutron-rich Mg region between N=20 and 28 New shell structures – onset of deformation Systematic HFB calculation M.V. Stoitsov et al., Phys. Rev. C68(2003) 054312 D1S R. Rodríguez-Guzmán et al., NPA709(2002)201

  5. Uniqueness in neutron-rich nuclei Shallow Fermi level • Spatially extended structure of the single-(quasi)particle wave functions Neutron skins and halos • New shell structures • Appearance of new magic numbers/disappearance of traditional magic numbers New regions of deformation “Pairing anti-halo effect” • Pairing in the continuum K.Bennaceur et al., PLB496(2000)154 • Changes the spatial structure of the quasiparticle wave functions • Emerges the di-neutron correlation M.Yamagami, PRC72(2005)064308 M.Matsuo et al., PRC71(2005)064326

  6. Collective modes unique in deformed neutron-rich nuclei Neutron excess • IS and IV mixing modes • Neutron-excitation dominant modes • Neutron-skin excitation modes Deformation Mixing of modes with different angular momenta In deformed neutron-rich nuclei with superfluidity Quadrupole vib. Monopole vib. ?? + Pairing vib.

  7. Continuum Deformation Pairing Microscopic model required Collective excitation modes =coherent superposition of 2qp (1p-1h) excitations Neutron excess Stable nuclei Drip-line nuclei Self-consistency

  8. Theoretical framework – quasiparticles in a deformed potential The coordinate-space Hartree-Fock-Bogoliubov theory J.Dobaczewski, H.Flocard and J.Treiner, NPA422(1984)103 A.Bulgac, FT-194-1980 (Institute of Atomic Physics, Bucharest) Cf. BCS Unphysical nucleon-gas problem in drip-line nuclei One can properly treat the pairing correlation in the continuum. • Mean-field Hamiltonian • Pairing field mixed-type delta interaction SkM* interaction We solve the HFB equations directly on the 2D lattice. 11-point formula for derivative • Simple • Appropriate for describing the spatially extended structure of wavefunctions H.O. basis 0

  9. Theoretical framework – quasiparticle RPA KY, N.Van Giai, PRC78(2008)064316 HFB equations Quasiparticle basis Residual interactions • particle-hole channel: We neglect the residual spin-orbit and Coulomb interactions. • particle-particle channel:

  10. Neutron-rich Mg isotopes beyond N=20 SkM*+mixed-type pairing (V0=-295 MeV fm3) Isoscalar transition strengths

  11. Intrinsic transition densities to the excited 0+ state g.s. half density positive trans. density negative trans. density

  12. Low-energy spectra Sensitive to the shell structure Experiments 34Mg: K.Yoneda et al., PLB499(2001)233 36Mg: A.Gade et al., PRL99(2007)072502 Microscopically calculated

  13. Quadrupole excitations KY, M.Yamagami, K.Matsuyanagi, NPA 779(2006)99 KY, arXiv:0902.3053

  14. Mechanism of the soft K=0+ mode KY, M.Yamagami, PRC77(2008)044312 34Mg 40Mg [202]3/2 [303]7/2 22 28 [321]3/2 [310]1/2 Two level model (Bohr-Mottelson) Ground state Excited state Opposite sign Enhancement Transition matrix element

  15. Neutron-pair transition strengths in 34Mg Monopole pairing Quadrupole pairing

  16. Prolate orbital Oblate orbital Neutron-rich Cr and Fe isotopes at around N=40 Potential energy surfaces (SkM*) Neutron single-particle energies of 64Cr The HFB solver “HFBTHO” (v1.66p) M.Stoitsov et al., Comp.Phys.Comm.167(2005)43

  17. Soft K=0+ mode in neutron-rich Cr and Fe isotopes KY and M.Yamagami, PRC77(2008)044312 Deformed-WS+Bogoliubov+QRPA N=40

  18. Magicity at N=20 J.A.Church et al.,PRC72(2005)054320 • Low-lying 2+ state: 885keV(32Mg), 659keV(34Mg) • Large B(E2;0+→2+): 447e2fm4(32Mg), 541e2fm4(34Mg) Breaking of the N=20 spherical magic number Shell inversion T.Motobayashi et al.,PLB346(1995)9 Importance of the continuum coupling and pair correlations, M.Yamagami and N.Van Giai, PRC69(2004)034301

  19. The island of inversion E.K.Waburton et al., PRC41(1990)1147 N=20 Y.Utsuno et al., PRC64(2001)011301R Where is the border located? What is the signature? • The gyromagnetic factor measurement • The beta-decay study of 33Mg P.Himpe et al., PLB643(2006)257 V.Tripathi et al., PRL101(2008)142504 “33Al has a certain amount of the 2p2h intruder configuration” The electric quadrupole moment Direct information on the nuclear deformation T.Nagatomo et al., ENAM’08 conference has been measured at GANIL.

  20. Particle-vibration coupling Microscopic particle-vibration coupling model Solutions of the Skyrme-HFB+QRPA equations Change of the density due to the collective vibrations To first order in the change of the density, the difference of the potential is evaluated to be

  21. Particle-vibration coupling The vacuum is defined as The density variation In a second quantized form using the RPA modes The coupling interaction can be derived from the Skyrme EDF. In the present calculation, the Landau-Migdal approximation is employed. The Landau-Migdal parameters are seen in N.Van Giai, H.Sagawa, PLB106(1981)379

  22. Description of odd A nuclei The nuclear Hamiltonian is diagonalized within the subspace The eigenstate of the odd-A systems: The electric quadrupole moment:

  23. Quadrupole moment of neutron-rich Al isotopes SkM*+mixed-type pairing (V0=-295 MeV fm3) KY, PRC79(2009)054303 spherical Experiment 31Al at RIKEN: D. Nagae et al., PRC79(2009)027301

  24. Summary 2D-Skyrme Hartree-Fock-Bogoliubov + quasiparticle RPA • Deformed ground state in 34,36,38,40Mg • Giant monopole resonance Two-peak structure at around 15 MeV and 25 MeV Mixed with GQR (K=0) • Soft K=0+ mode especially in 34,40Mg Sensitive to the neutron number (shell structure around the Fermi level) In the deformation region, where the orbitals both of up-sloping and of down-sloping exist. The coherent coupling between the pairing vibration and the beta vibration of neutrons • Core polarization in 31,33,35Al Neutron pairing correlations across N=20 play an important role for the polarization effect.

  25. Perspectives • Neutron-pair transition strengths Matrix elements for the 2qp transition The upper components of the HFB wavefunctions In drip-line nuclei, it is strongly affected by the continuum. A good tool for investigating the continuum

  26. New kinds of resonancesin deformed drip-line nuclei Isoscalar neutron The lower-lying resonance consists of two modes. • Resonance associated with the K=0 component of the GQR • (Non-collective) Neutron excitation mode

  27. d5/2 s1/2 • Novel picture of single-(quasi)particles “s-wave dominance” in weak binding T.Misu et al.,NPA614(1997)44 I.Hamamoto, PRC69,041306 (2004)

  28. p-h (2qp) excitations into the continuum • pairing correlations in the continuum s-wave dominant levels in the continuum?? The Gamow state in a deformed potential KY and K.Hagino, PRC72(2005)064311

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