slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
多体共鳴状態の境界条件によって解析した 3α 共鳴状態の構造 PowerPoint Presentation
Download Presentation
多体共鳴状態の境界条件によって解析した 3α 共鳴状態の構造

Loading in 2 Seconds...

play fullscreen
1 / 24

多体共鳴状態の境界条件によって解析した 3α 共鳴状態の構造 - PowerPoint PPT Presentation


  • 204 Views
  • Uploaded on

多体共鳴状態の境界条件によって解析した 3α 共鳴状態の構造. C. Kurokawa 1 and K. Kato 2 Meme Media Laboratory, Hokkaido Univ., Japan 1 Div. of Phys., Grad. Sch. of Sci., Hokkaido Univ., Japan 2. Theoretical studies of 12 C. D.M.Brink in Proceedings of the Fifteen Solvay Conference on Physics (19070)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '多体共鳴状態の境界条件によって解析した 3α 共鳴状態の構造' - kellan


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

多体共鳴状態の境界条件によって解析した3α共鳴状態の構造多体共鳴状態の境界条件によって解析した3α共鳴状態の構造

C. Kurokawa1 and K. Kato2

Meme Media Laboratory, Hokkaido Univ., Japan1

Div. of Phys., Grad. Sch. of Sci., Hokkaido Univ., Japan2

theoretical studies of 12 c
Theoretical studies of 12C

D.M.Brink in Proceedings of the Fifteen Solvay Conference on Physics (19070)

○Microscopic 3α model (RGM・GCM・OCM)

Y.Fukushima and M.Kamimura in Proceedings of the International Conference on Nuclear Structure (1977)

M.Kamimura, Nucl. Phys. A351(1981),456

Y.Fujiwara, H.Horiuchi, K.Ikeda, M.Kamimura, K.Katō, Y.Suzuki and E.Uegaki, Prog Theor. Phys. Suppl.

68 (1980)60.

E.Uegaki, S.Okabe, Y.Abe and H.Tanaka, Prog. Theor. Phys. 57(1977)1262; 59(1978)1031; 62(1979)1621.

H.Horiuchi, Prog. Theor. Phys. 51(1974)1266; 53(1975)447.

K.Fukatsu, K.Katō and H.Tanaka, Prog. Theor. Phys.81(1988)738.

○3α+p3./2Closed shell

N.Takigawa, A.Arima, Nucl. Phys. A168(1971)593.

N.Itagaki Ph.D thesis of Hokkaido University (1999)

Y.Kanada-En’yo, Phys. Rev. Lett. 24(1998)5291.

○Deformation (Mean-Field)

G.Leander and S.E.Larsson, Nucl. Phys.A239(1975)93.

○Faddeev

Y.Fujiwara and R.Tamagaki Prog. Theor. Phys. 56(1976)1503.

H.Kamada and S.Oryu, Prog. Theor. Phys 76(1986)1260.

α

α

α

31-

Γ=34keV

α

02+

α

Γ=8.7eV

3

α

01+

Excited states of cluster states?

situation around e x 10 mev

0+, 2+

Situation around Ex= 10 MeV

Energy level of 12C

a

l=0

02+ :

a

L=0

a

Alpha-condensed state

A.Tohsaki et al., PRL87(2001)192501

Can 3αModel reproduce both of the 22+ and the 03+ states ?

What kind of structure dose the 03+ state have ?

Why 03+ has such a large width ?

0+ : Er=2.7+0.3 MeV, G= 2.7+0.3 MeV

2+ : Er=2.6+0.3 MeV, G= 1.0+0.3 MeV

[Ref.]: M.Itoh et al., NPA 738(2004)268

[Ref.] E.Uegaki et al.,PTP57(1979)1262

Boundary condition for three-body resonances

Analysis of decay widths

our strategy
Our strategy

In order to taking into account the boundary condition for three-body

resonances, we adopted the methods to 3 Model;

  • Complex Scaling Method (CSM)

[Ref.] J.Aguilar and J.M.Combes, Commun. Math. Phys., 22(1971),269

E.Balslev and J.M.Combes, Commun. Math. Phys., 22(1971),280

  • Analytic Continuation in the Coupling Constant

[Ref.] V.I.Kukulin, V.M.Krasnopol’sky, J.Phys. A10(1977),

combined with the CSM (ACCC+CSM)

[Ref.] S.Aoyama PRC68(2003),034313

Both enables us to obtain not only resonance energy but also total decay width

model 3 orthogonality condition model ocm

a2

a2

a2

a1

a1

a1

c=3

c=1

c=2

a3

a3

a3

Model : 3  Orthogonality Condition Model (OCM)

folding for Nucleon-Nucleon interaction(Nuclear+Coulomb)

[Ref.]:E. W. Schmid and K. Wildermuth, Nucl. Phys. 26 (1961) 463

, -parity )

μ=0.15 fm-2

: OCM [Ref.]: S.Saito, PTP Supple. 62(1977),11

Phase shifts and Energies of 8Be, and Ground band states of 12C

,

[Ref.]: M.Kamimura, Phys. Rev. A38(1988),621

methods for treatment of three body resonant states

Exp. Broad state

Methods for treatment of three-body resonant states
  • CSM

It is sometimes difficult for CSM

to solve states with quite large

decay widths due to the limitation

of the scaling angle  and finite

basis states.

In order to search for the broad 0+ state, we employed …

  • ACCC+CSM

k

Im(k)

δ→0

: Atractive potential with < 0

Re(k)

Resonance

energy levels obtained by csm and accc csm

03+: Er=1.66 MeV, Γ=1.48 MeV

22+: Er=2.28 MeV, Γ=1.1 MeV

0+ : Er=2.7+0.3 MeV, G= 2.7+0.3 MeV

2+ : Er=2.6+0.3 MeV, G= 1.0+0.3 MeV

[Ref.]: M.Itoh et al., NPA 738(2004)268

Energy levels obtained by CSM and ACCC+CSM

G= 0.375+0.040 MeV

Γ=0.12 MeV

(2+)

ACCC+CSM

3α Model reproduce 22+ and 03+ in the same energy region by taking into account the correct boundary condition

E.Uegaki et al.,PTP(1979)

structures of 0 states through amplitudes
Structures of 0+ states through Amplitudes

Wave function of 0+ states

Y(12C) Jp=0+ = al=0,L=0j0,0 + al=2,L=2j2,2 + al=4,L=4j4,4

8Be

jl,L= [ 8Be (l) x L ]

a

l

a

al,L2: Channel Amplitudes

L

a

Channel Amplitudes of 01+, 02+ and 04+

feature of the broad 3 rd 0 state
Feature of the broad 3rd 0+ state

Channel amplitudes as a function of 

8Be

a

l=0

a

L=0

2

Dominated

2

a

2

Similar property to 02+( Rr.m.s= 4.29 fm)

Re(Rr.m.s) (d= -140): 5.44 fm

Large component of a0,02makes suchthe large width.

Wave function of 03+ shows similar properties to 02+.

03+ is considered as an excited state of 02+. Higher nodal state of 02+ ?

summary of obtained 0 states

I=0

I=0

L=0

but higher nodal ?

L=0

Summary of obtained 0+ states

04+

03+

02+

r.m.s.=4.29 fm

structure of the 0 4 state
Structure of the 04+ state

4th 0+ state ;

Large component of high angular momentum compared with 2nd 0+

a0,02 =0.499,a2,22 =0.307,a4,42 =0.194

Total decay width is sharp: Er=4.58 MeV, =1.1 MeV

  • 3αOCM with SU(3) base : K.Kato, H.Kazama, H.Tanaka, PTP 77(1986),185.

Component of linear-chain configuration: 56%

  • AMD: Y.Kanada-En’yo, nutl-th/0605047.

FMD: T.Neff, H.Feldmeier, NPA 738(2004), 357.

Linear chain like structure is found

α

α

α

probability density of 1 st 0 and 4 th 0 states preliminary
Probability Density of 1st 0+ and 4th 0+ states (Preliminary)

Probability Density of ’s

r1

r2

r1 = r2 = r

q12

01+

r [fm]

04+

q12

q12

summary and future work
Summary and Future work
  • We solve states above 3αthresold energy taking into account the boundary condition for three-body resonant states.
  • Obtained resonance parameters of many J states reproduce experimental data well.
  • We obtained broad 3rd 0+ state near the 2nd 2+ state. The state has similar structure to the 2nd 0+ state. It is thus expected to be an excited state of 2nd 0+.
  • The 4th 0+ state has large component of high angular momentum channel, [8Be (2+) x L=2],and has a sharp decay width.

These features reflect the linear-chain like structure of 3αclusters. Members of rotational band built upon the 4th 0+ state ?

  • How do these states contribute to the real energy ? To investigate it we calculate the Continuum Level Density in the CSM and partial decay widths to 8Be(0+, 2+, 4+)+α in feature.

[Ref.] A.T. Kruppa and K. Arai, PLB 431(1998)237

R. Suzuki, T. Myo, and K. Kato, PTP 113 (2005) 1273

contributions from resonant states to real energy
Contributions from resonant states to real energy

Continuum Level Density (CLD) Δ(E) [Ref.] S.Shomo, NPA 539 (1992) 17.

δl: phase shift

Discretization with a finite number N of basis functions

[Ref.] A.T. Kruppa and K. Arai, PLB 431(1998)237.

Smoothing technique is needed,

but results depend on smoothing parameter.

cld in the complex scaling method ref r suzuki t myo and k kato ptp 113 2005 1273
CLD in the Complex Scaling Method[Ref.] R. Suzuki, T. Myo, and K. Kato, PTP 113 (2005) 1273

Bound state

Continuum

Resonance

ER, εc(θ) have complex eigenvalues in CSM

CLD in CSM:

Smoothing technique is not needed

application to system
Application to 3α system

CLD of 3αsystem

α2

α1

continuum level density 0 states
Continuum Level Density: 0+ states

8Be(0+) +α

8Be(2+) +α

E [MeV]

subtraction of contribution from 8 be
Subtraction of contribution from 8Be+α

8Be

α2

  • α1- α2: resonance + continuum
  • (α1α2)- α3: continuum

α1

α3

  • α1- α2: continuum
  • (α1α2)- α3: continuum
search for broad 0 state with
Search for broad 0+ state with

δ= -150 MeV

δ= -110 MeV

δ= -50 MeV

03+

04+

05+

04+

04+

05+

03+

δ= -200 MeV

δ= -250 MeV

04+

05+

trajectories of the broad 0 3 state
Trajectories of the broad 03+ state

Complex-Energy plane

Complex-Momentum plane

Obtained resonance parameter

methods for treatment of three body resonant states1
Methods for treatment of three-body resonant states
  • Complex Scaling Method (CSM)

It is sometimes difficult for CSM to solve state with a quite large decay width due to the limitation of the scaling angle .

In order to search for the broad 0+ state, we employed …

  • Analytic Continuation in the Coupling Constant combined with the CSM (ACCC+CSM)

ACCC+CSM

CSM

k

k

Im(k)

Im(k)

Branch cut

Bound state

δ→0

Re(k)

Re(k)

q

Anti-bound state

Resonance

Resonance