How Exotic Cluster Configuration Affectsthe Collective Motion in Nuclei

Xi-Guang Cao（曹喜光）

Collaborators: Yu-Gang Ma（马余刚）, Wan-Bing He（何万兵）,

Xiang-Zhou Cai（蔡翔舟）, Guo-Qiang Zhang（张国强）

2014 Annual meeting of Sub-committee of Nuclear Physics of Shanghai Nuclear Society Shanghai, Nov. 27, 2014

Outline:

Background & method introduction Nuclear cluster in light nuclei

Nuclear collective motion

Microscopic dynamical model

GDR algorithm & verification

Results and discussions Density distribution of cluster nuclei and wave packets

GDR of 8Be, 12C & 16O with different α configurations

Summary

Background & method introduction-- cluster in light nuclei

Cluster complete with mean field widely in light nucleiFar from β stability line, the cluster phenomenon appears as halo

11Be

W. Nörtershäuser,PRL 102, 062503 (2009)

Cluster is predicted to appear near cluster decay threshold inα conjugate nuclei

K. Ikeda, N. Takigawa, H. Horiuchi, Prog. Theor. Phys. Suppl. Extra Number, 464 (1968)

The α cluster is the most prominentcase since (1) the high bindingenergy of α and (2) high energy offirst excitation state

The α cluster configuration in 12C

Marin-Lámbarri D. J, Bijker R, Freer M, et al. Evidence for Triangular D3h Symmetry in 12C. Phys Rev Lett. 113,012502 (2014)

New data supports the triangle α configuration of 12C Hoyle state

AB initio calculation based on effective field theoryobtains that Hoyle state is more like a linear chain of three alpha clusters

Evgeny Epelbaum et al., Phys. Rev. Lett. 106, 192501 (2011)

Non-localized, condensed like wave function, gas of α clusterin Hoyle state

THSR wave function:A. Tohsaki et al., Phys. Rev. Lett. 87, 192501 (2001)T. Suhara et al., Phys. Rev. Lett. 112,062501 (2014)

M. Chernykh, et al., Phys. Rev. Lett. 98 (2007) 032501

Algebraic model: Bijker R, Iachello F. Evidence for Tetrahedral Symmetry in O16. Phys Rev Lett. 112, 152501 (2014) Effective field theory: E. Epelbaum, H. Krebs, T. A. Lahde, D. Lee, U.-G. Meißner, and G. Rupak, Phys. Rev. Lett. 112, 102501 (2014)Covariant density functional theory: L. Liu and P. W. Zhao, Chin. Phys. C 36, 818 (2012)

The α cluster configuration in 16O

Many different calculations support thetetrahedral structure in 16O ground state,Challenging the traditional shell model picture

The excited 16O may evolve into square, or linear chain, oror non-localized gas configuration

Covariant density functional theory: L. Liu and P. W. Zhao, Chin. Phys. C 36, 818 (2012)Effective field theory: Evgeny Epelbaum, Hermann Krebs, Timo A. Lähde, Dean Lee, Ulf-G. Meißner, and Gautam Rupak, Phys. Rev. Lett. 112, 102501 (2014)THSR wave function: T. Suhara et al., Phys. Rev. Lett 112,062501 (2014)

Bose α-particle gas ?or Condensate ?or geometric arrangement of α-particles ?If so how the α-particles are arranged?

α-particle correlations play a significant role in α cluster statesuch as Hoyle state , the correlation will essentially determine:

FMD

THSR

ACM, Algebraic modelEffective field theory

Condensate or gas probes ?Non-sequential α decay, α decay kinetics

O.S. Kirsebom, et al., Phys. Rev. Lett. 108 (2012) 202501. J T.K. Rana, et al., Phys. Rev. C 88 (2013) 021601(R). Manfredi, et al., Phys. Rev. C 85 (2012) 037603.

or geometric arrangement ?Rotation band associated with D3 point group symmetry may provide the information about deformation

If so how the α-particles are arranged ?

Ad.R. Raduta, et al., Phys. Lett. B 705 (2011) 65.

An understanding of the excitations of the cluster stateis essential needed.

Two important points need to beexplored:From the experimental point of view, the effectiveprobe is need to diagnose the different configuration

What are the aspects of the collective dynamics of excited α clustering systems and the underlying mechanism?

Giant Resonance α Cluster Configuration

Centroid energy of GR can provide direct information about nuclear sizes and the nuclear equation of state

Width of GR closely relates with nuclear deformation, temperature, and angular momentum

Background & method introduction-- Giant Resonance

Microscopic descriptionMacroscopic description

Giant resonances are typical collective excitations in nuclei

Eγ Eγ

Valence neutron <=> Core Proton <=> Neutron

There are three main excitation mode: GDR, PDR, GMR

Background & method introduction-- microscopic dynamical model

11Be

1) Dynamical wave packet width in wave function (as in FMD).Taking into account the kinetic energy term of the momentum variance of wave packets to the Hamiltonian

The EQMD model

Y = Õi

fi

ri( )

firi( ) =

ni+n

i

*

2p

æ

èçç

ö

ø÷÷

3 4

exp -ni

2ri- R

i( )2

+i

Pi× ri

é

ëê

ù

ûú

H = Y -i

å2

2mÑi

2 -TÙ

c.m.+HÙ

int Y

=Pi

2

2m+

3 2 1+ li

2di

2( )4ml

i

é

ë

êê

ù

û

úú

i

å -Tc.m.

+Hint

T. Maruyama, et al., Phys Rev C, 1996, 53: 297-304.R. Wada et al., Phys. Lett. B 422, 6 471 (1998).

Compared with other MD models: QMD, IQMD, AMD, CoMD(Italy), ImQMD (CIAE, Beijing), IDQMD (Shanghai), LQMD (Lanzhou), has the following features:

z {Ri ,Pi,li,di,R

i,

.

P.

i ,li

.

,di

.

}æ

èç

ö

ø÷ º Y i

d

dt-H

Ù

Y

d z dt = 0t1

t2

ò

Hint

= HSkyrme

+HCoulomb

+HSymmetry

+HPauli

HSkyrme

=a

2r0

r2ò r( )d 3r +b

g +1( )r0

grg+1ò r( )d 3r

HSymmetry

=cS

2r0

2d Ti ,Tj( ) -1é

ëùûò

i. j¹0

å ri

r( )rj

r( )d 3r

The equation motion of nucleon

The effective potential considered:

2) Including Pauli potential into effective interaction to approximate the nature of fermion many-body system

3) The initialization of ground nuclei: fraction cooling

HPauli

=cP

2fi- f

0( )i

åm

q fi- f

0( )

fiº d S

i,S

j( )j

å d Ti,Tj( ) f

ifj

2

Advantages: QMD based many-body model, mature and powerful Full microscopic, without assuming cluster in advance Without assuming reaction mechanism in advance Dynamical evolution -> links with observables directly Compared with TDHF cal., this method can be used at

higher energy, many-body correlations, more realistic linkage with observables

Disadvantages: Semiclassical No antisymmetrized

Unique Advantages of EQMD compared with other version QMD:

Energy conservation more better vs time evolutionStable enough ground state to study low energy region reaction

process, without spurious particle emissionDynamical wave packet evolution, reasonable fluctuation and dissipation

EQMD model can wellproduce the bulk propertiesof isotopes acrossthe whole nuclear chart,including stable isotopesas well as isotopes far frombeta stability line

GDR algorithm & verification-- How to extract giant resonance from QMD

V. Baran et al, Nucl. Phys.A 679,373(2001)Fourier transformation

Dipole excitation

This approach has been successfully applied in GDR, PDR, GMRcalculations by IQMD & BUU model based on the fact that the quasiperiodic motion of nucleons in GR represents a known classical limit of quantum mechanic, which has be confirmed by TDHF calculations long before [A. S. Umar Phys. Rev. C 32, 172 (1985)].

GDR algorithm & verification-- verification the reliability of EQMD in GDR calculations

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4Ne20_C12_145MeV

out event plane

in event plane

all

data

CASCADE

cuts 100±5 hbar cuts 60±5 hbar cuts >95 hbar

The data is from D. Pandit et al, Phys. Rev. C 81, 061302 (2010)

GDR in fusion reaction

Results & discussions-- Density distribution of cluster nuclei and wave packets

Binding energy of nuclei with cluster configuration

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25B e8

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

C 12_chain

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25C 12_triangle

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25O 16_chain

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25

O 16_kite

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25

O 16_square

nuclear m atter density at Z=0

Density of each nucleon in nuclei with alpha cluster configuration

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

C 12_chain

nuclear m atter density at Z=0

X (fm)-10 -8 -6 -4 -2 0 2 4 6 8 10

Y (

fm)

-6

-4

-2

0

2

4

6

0

0.05

0.1

0.15

0.2

0.25O 16_chain

nuclear m atter density at Z=0

Results & discussions-- GDR of 8Be, 12C & 16O with different α configurations

Dipole evolution of 16O

(M eV )gE10 20 30 40 50

dP/dE (arb.units)

0

1O no cluster16

S .B acca et al.A hrens et al.O16

(mb)

gs

0

10

20

30

16O ground state withtetrahedron

16O ground state withoutcluster

EQMD calculation supports 16O ground state with tetrahedron

12C GDR without (left panel) and with (right panel)

cluster configuration with data.

EQMD calculation indicates the ground of 12C is a multiconfiguration mixing of shell-model-like and cluster-likeconfigurations,which is consistent with the prediction of AMD [Y. Kanada-En’yo, Phys. Rev. Lett 81, 5291 (1998)] and FMD [M. Chernykh, H. Feldmeier et al., Phys. Rev. Lett. 98, 032501 (2007)]

GDR spectrum is highly fragmented into several apparent peaks due to theα structure The different α clusterconfigurations in 12C and 16Ohave correspondingcharacteristic spectra of GDR The number and centroid energies of peaks in the GDRspectra can be reasonablyexplained by the geometricaland dynamical symmetries ofα clustering configurations

Correspondence between GDR and α cluster configurations

GDR spectrum is highly fragmented into several apparent peaks due to theα structure The different α clusterconfigurations in 12C and 16Ohave correspondingcharacteristic spectra of GDR The number and centroid energies of peaks in the GDRspectra can be reasonablyexplained by the geometricaland dynamical symmetries ofα clustering configurations

Correspondence between GDR and α cluster configurations

Dynamical evolution of density profile -- 8Be, 12C and 16O

The α cluster is very different from free αparticle

Binding energy evolution between two alphas in 8Be

Hints from a experimental point of view--- sensitive probe

The measurement of the GDR peak located around 30 MeVis a feasible way to confirm the existence of an α clustering state

Analysis of other low- lying peaks can be used to diagnose thedifferent configurations formed by α clusters

The similar GDRs of 8Be and triangle 12C appear as substructuresin the GDRs of chain 12C and kite 16O, respectively, which will helpto recognize the α configuration in 12C and 16O

Summary & outlook

The semiclassical QMD like model is suitable to study GR

The GDR of excited state with α cluster is studied by EQMD

GDR as an effective probe of α configuration• Peak near 30 MeV• Substructure in 12C and 16O

The density evolution shows the complicated underlyingdynamics of α cluster in nuclei

Potential experimental chance on HIγS (Triangle Uni.) andSLEGS (SINAP)

Thanks for the discussions with P. Schuck, T. Maruyama

J. Natowitz, S. Shlomo and R. Wada for this work.