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@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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slide1

@Saclay

18-20 May, 2009

Collective modes of excitation in deformed neutron-rich nuclei

Kenichi Yoshida

slide2

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
slide3

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

slide4

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

slide5

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

slide6

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.

slide7

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

slide8

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

slide9

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:
slide10

Neutron-rich Mg isotopes beyond N=20

SkM*+mixed-type pairing (V0=-295 MeV fm3)

Isoscalar transition strengths

slide11

Intrinsic transition densities to the excited 0+ state

g.s. half density

positive trans. density

negative trans. density

slide12

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

slide13

Quadrupole excitations

KY, M.Yamagami, K.Matsuyanagi, NPA 779(2006)99

KY, arXiv:0902.3053

slide14

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

slide15

Neutron-pair transition strengths in 34Mg

Monopole pairing

Quadrupole pairing

slide16

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

slide17

Soft K=0+ mode in neutron-rich Cr and Fe isotopes

KY and M.Yamagami, PRC77(2008)044312

Deformed-WS+Bogoliubov+QRPA

N=40

slide18

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

slide19

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.

slide20

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

slide21

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

slide22

Description of odd A nuclei

The nuclear Hamiltonian

is diagonalized within the subspace

The eigenstate of the odd-A systems:

The electric quadrupole moment:

slide23

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

slide24

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.

slide25

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

slide26

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
slide27

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)

slide28

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