Collective modes of excitation in deformed neutron-rich

nuclei

Kenichi Yoshida

@Saclay 18-20 May, 2009

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

Uniqueness in neutron-rich nucleiShallow Fermi level

Spatially extended structure of the single-(quasi)particle wave functions

New shell structuresAppearance of new magic numbers/disappearance of traditional

magic numbersNew regions of deformation

Neutron skins and halos

Weak bindingContinuum coupling

M.V

. Sto

itsov

et a

l., P

hys.

Rev

. C68

(200

3) 0

5431

2

Neutron-rich Mg region between N=20 and 28

Systematic HFB calculation

R. Rodríguez-Guzmán et al., NPA709(2002)201

New shell structures – onset of deformation

D1S

Shallow Fermi level

Spatially extended structure of the single-(quasi)particle wave functions

New shell structuresAppearance of new magic numbers/disappearance of traditional

magic numbersNew regions of deformation

Neutron skins and halos

Pairing in the continuum

M.Yamagami, PRC72(2005)064308

M.Matsuo et al., PRC71(2005)064326

Changes the spatial structure of the quasiparticle wave functions

Emerges the di-neutron correlation

F

Uniqueness in neutron-rich nuclei

“Pairing anti-halo effect”K.Bennaceur et al., PLB496(2000)154

Collective modes unique in deformed neutron-rich nuclei

Neutron excessIS and IV mixing modesNeutron-excitation dominant modesNeutron-skin excitation modes

DeformationMixing of modes with different angular momenta

Quadrupole vib.

Monopole vib.

+ Pairing vib.

In deformed neutron-rich nuclei with superfluidity

??

Continuum

PairingDeformation

Self-consistency

F

Collective excitation modes=coherent superposition of 2qp (1p-1h) excitations

Stable nuclei

F

Drip-line nuclei

Neutron excess

Microscopic model required

J.Dobaczewski, H.Flocard and J.Treiner, NPA422(1984)103A.Bulgac, FT-194-1980 (Institute of Atomic Physics, Bucharest)

Cf. BCS Unphysical nucleon-gas problem in drip-line nuclei

Mean-field Hamiltonian Pairing field

mixed-type delta interactionSkM* interaction

One can properly treat the pairing correlation in the continuum.

The coordinate-space Hartree-Fock-Bogoliubov theory

z

0

11-point formula for derivative

Simple Appropriate for describing the spatially extended

structure of wavefunctions H.O. basis

We solve the HFB equations directly on the 2D lattice.

Theoretical framework – quasiparticles in a deformed potential

Quasiparticle basisHFB equations

particle-hole channel:

We neglect the residual spin-orbit and Coulomb interactions.

particle-particle channel:

Residual interactions

KY, N.Van Giai, PRC78(2008)064316Theoretical framework – quasiparticle RPA

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

34Mg 36Mg 38Mg 40Mg

0.35 0.31 0.29 0.28

0.41 0.39 0.38 0.362,n

2,p

Isoscalar transition strengths

Intrinsic transition densities to the excited 0+ state

g.s. half density

positive trans. density

negative trans. density

Sensitive to the shell structure

Microscopically calculated

Experiments34Mg: K.Yoneda et al., PLB499(2001)23336Mg: A.Gade et al., PRL99(2007)072502

Low-energy spectra

Quadrupole excitations

0K

2K

KY, arXiv:0902.3053

34Mg 36Mg 38Mg 40Mg

1.57 1.58 1.82 1.91

1.41 1.41 1.55 1.79

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

Mechanism of the soft K=0+ mode

34Mg 40Mg

22 28

KY, M.Yamagami, PRC77(2008)044312

[321]3/2

[202]3/2

[310]1/2

[303]7/2

Ground state

Excited state

Transition matrix element

Opposite sign Enhancement

Two level model (Bohr-Mottelson)

Neutron-pair transition strengths in 34MgMonopole pairing Quadrupole pairing

Neutron single-particle energies of 64Cr Potential energy surfaces (SkM*)

M.Stoitsov et al., Comp.Phys.Comm.167(2005)43The HFB solver “HFBTHO” (v1.66p)

Prolate orbital

Oblate orbital

Neutron-rich Cr and Fe isotopes at around N=40

N=40

KY and M.Yamagami, PRC77(2008)044312

0KDeformed-WS+Bogoliubov+QRPA

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

Magicity at N=20J.A.Church et al.,PRC72(2005)054320

Low-lying 2+ state: 885keV(32Mg), 659keV(34Mg)Large B(E2;0+→2+): 447e2fm4(32Mg), 541e2fm4(34Mg)

T.Motobayashi et al.,PLB346(1995)9

Breaking of the N=20 spherical magic number

Shell inversion

Importance of the continuum coupling and pair correlations, M.Yamagami and N.Van Giai, PRC69(2004)034301

The island of inversionY.Utsuno et al., PRC64(2001)011301R

N=20

Where is the border located?What is the signature?

The gyromagnetic factor measurementThe beta-decay study of 33Mg V.Tripathi et al., PRL101(2008)142504

P.Himpe et al., PLB643(2006)257

“33Al has a certain amount of the 2p2h intruder configuration”

The electric quadrupole momentDirect information on the nuclear deformation

has been measured at GANIL. T.Nagatomo et al., ENAM’08 conference

E.K.Waburton et al., PRC41(1990)1147

Particle-vibration couplingMicroscopic 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

Particle-vibration couplingThe 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.

N.Van Giai, H.Sagawa, PLB106(1981)379The Landau-Migdal parameters are seen in

Description of odd A nucleiThe nuclear Hamiltonian

is diagonalized within the subspace

The eigenstate of the odd-A systems:

The electric quadrupole moment:

Quadrupole moment of neutron-rich Al isotopesKY, PRC79(2009)054303SkM*+mixed-type pairing (V0=-295 MeV fm3)

spherical

Experiment31Al at RIKEN: D. Nagae et al., PRC79(2009)027301

Summary

Deformed ground state in 34,36,38,40Mg

Soft K=0+ mode especially in 34,40MgSensitive 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

2D-Skyrme Hartree-Fock-Bogoliubov + quasiparticle RPA

Giant monopole resonanceTwo-peak structure at around 15 MeV and 25 MeV

Mixed with GQR (K=0)

Core polarization in 31,33,35AlNeutron pairing correlations across N=20 play an important role for the polarization effect.

Neutron-pair transition strengths

Matrix elements for the 2qp transition

The upper components of the HFB wavefunctions

Perspectives

In drip-line nuclei, it is strongly affected by the continuum.

A good tool for investigating the continuum

The lower-lying resonance consists of two modes.Resonance associated with the K=0 component of the GQR(Non-collective) Neutron excitation mode

New kinds of resonances in deformed drip-line nuclei

Isoscalarneutron

Novel picture of single-(quasi)particles

T.Misu et al.,NPA614(1997)44 I.Hamamoto, PRC69,041306 (2004)

d5/2

s1/2

“s-wave dominance” in weak binding

p-h (2qp) excitations into the continuumpairing correlations in the continuum

s-wave dominant levels in the continuum??

KY and K.Hagino, PRC72(2005)064311The Gamow state in a deformed potential