Theoretical Studies on Reaction Mechanisms of Unstable Nuclei - - PowerPoint PPT Presentation

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Theoretical Studies on Reaction Mechanisms of Unstable Nuclei - - PowerPoint PPT Presentation

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Theoretical Studies on Reaction Mechanisms of Unstable Nuclei Kazuyuki Ogata Department of Physics, Kyushu University You are here. Outline 0) Brief introduction to CDCC M. Kamimura, Yahiro, Iseri, Sakuragi, Kameyama and Kawai, PTP Suppl. 89 ,

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Theoretical Studies on Reaction Mechanisms of Unstable Nuclei

Kazuyuki Ogata

Department of Physics, Kyushu University

You are here.

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Outline

0) Brief introduction to CDCC 1) Four-body breakup processes for 6He induced reaction

  • M. Kamimura, Yahiro, Iseri, Sakuragi, Kameyama and Kawai, PTP Suppl. 89, 1 (1986);
  • N. Austern, Iseri, Kamimura, Kawai, Rawitscher and Yahiro, Phys. Rep. 154 (1987) 126.

2) Microscopic description of projectile breakup processes 3 New approach to inclusive breakup processes

  • T. Matsumoto, Hiyama, O., Iseri, Kamimura, Chiba, Yahiro, PRC70, 061601(R) (2004);
  • T. Matsumoto, Egami, O., Iseri, Kamimura, Yahiro, PRC73, 051602 (R) (2006);
  • T. Egami, Matsumoto, O., Yahiro, PTP 121, 789 (2009).
  • K. Minomo, O., Shimizu, Kohno, Yahiro, J Phys. G 37, 085011 (2010).
  • S. Hashimoto, O., Chiba, Yahiro, PTP 122, 1291 (2009);
  • T. Ye, Watanabe, O., Chiba, PRC78, 024611 (2008);
  • T. Ye, Watanabe, O., PRC80, 014604 (2009).
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The Continuum-Discretized Coupled Channels method (CDCC)

Truncation and Discretization

(k) 0(k0) 0(k0) i

^

m ax

C D C C

ˆ ˆ ˆ ( , ) ( ) ( , )

i i i i i

r R r K R   

     

R (K) r (k)   a A c x

m ax 1

1

ˆ ˆ ( , ) ( , ) ( , ) ( , ) ( , )

i i

i k i k i

r R k r K R K R k r dk     

  

     

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Outline

0) Brief introduction to CDCC 1) Four-body breakup processes for 6He induced reaction

  • M. Kamimura, Yahiro, Iseri, Sakuragi, Kameyama and Kawai, PTP Suppl. 89, 1 (1986);
  • N. Austern, Iseri, Kamimura, Kawai, Rawitscher and Yahiro, Phys. Rep. 154 (1987) 126.

2) Microscopic description of projectile breakup processes 3 New approach to inclusive breakup processes

  • T. Matsumoto, Hiyama, O., Iseri, Kamimura, Chiba, Yahiro, PRC70, 061601(R) (2004);
  • T. Matsumoto, Egami, O., Iseri, Kamimura, Yahiro, PRC73, 051602 (R) (2006);
  • T. Egami, Matsumoto, O., Yahiro, PTP 121, 789 (2009).
  • K. Minomo, O., Shimizu, Kohno, Yahiro, J Phys. G 37, 085011 (2010).
  • S. Hashimoto, O., Chiba, Yahiro, PTP 122, 1291 (2009);
  • T. Ye, Watanabe, O., Chiba, PRC78, 024611 (2008);
  • T. Ye, Watanabe, O., PRC80, 014604 (2009).
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Energy of 6He 0.97MeV(g.s.)

4-body CDCC

 Discretization of 6He W. Fn. by diagonalizing internal Hamiltonian.  Gaussian Expansion Method (GEM)

 6He = + +

4He

n n

4He

n n

4He

n n

0+ 1 2+ Discretized continuum states!

max

CDCC

  • 4

ˆ ˆ

i i i i 

 

4-body W. Fn.

3-body structure of 6He C.M. motion between 6He and A

  • T. Matsumoto, Hiyama, O., Iseri, Kamimura, Chiba, Yahiro,

PRC70, 061601(R) (2004).

 Diagonalization of internal Hamiltonian

Hiyama, Kino, Kamimura,

  • Prog. Part. Nucl. Phys. 51, 223 (2003).

37 44 53

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Virtual 4-body breakup of 6He by 209Bi

3-body CDCC 4-body CDCC 4-body CDCC w/o BU Aguilera et al.

  • T. Matsumoto, Egami, O., Iseri, Kamimura, Yahiro,

PRC73, 051602 (R) (2006).

Key points  4-body CDCC reproduces well the data.  3-body CDCC not.  Virtual breakup of 6He is important. New topic  4-body CDCC based on binning method

  • M. Rodriguez-Gallardo, Arias, Gomez-Camacho, Moro,

Thompson, PRC80, 051601 (R) (2009).

Future work  Systematic analysis of 4-body breakup  5-body and 6-body CDCC (with COSM)

6He-208Pb at 22 MeV 6He-209Bi at 22.5 MeV

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SLIDE 7

Real 4-body breakup of 6He

  • T. Egami, Matsumoto, O., Yahiro, PTP121, 789 (2009).

Key points  Smoothing discrete observables  Simple Lorenzian procedure fails.  A smoothing method with L-S Eq. works. New topic  Complex-scaled smoothing method

  • T. Matsumoto, Kato, Yahiro, arXiv:1006.0668 (2010).

Future work  Direct comparison with exp. data

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Real 4-body breakup of 6He

  • T. Egami, Matsumoto, O., Yahiro, PTP121, 789 (2009).

Key points  Smoothing discrete observables  Simple Lorenzian procedure fails.  A smoothing method with L-S Eq. works. New topic  Complex-scaled smoothing method

  • T. Matsumoto, Kato, Yahiro, arXiv:1006.0668 (2010).

Future work  Direct comparison with exp. data

  • M. Rodriguez-Gallardo, Arias, Gomez-Camacho,

Moro, Thompson, PRC80, 051601 (R) (2009).

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Outline

0) Brief introduction to CDCC 1) Four-body breakup processes for 6He induced reaction

  • M. Kamimura, Yahiro, Iseri, Sakuragi, Kameyama and Kawai, PTP Suppl. 89, 1 (1986);
  • N. Austern, Iseri, Kamimura, Kawai, Rawitscher and Yahiro, Phys. Rep. 154 (1987) 126.

2) Microscopic description of projectile breakup processes 3 New approach to inclusive breakup processes

  • T. Matsumoto, Hiyama, O., Iseri, Kamimura, Chiba, Yahiro, PRC70, 061601(R) (2004);
  • T. Matsumoto, Egami, O., Iseri, Kamimura, Yahiro, PRC73, 051602 (R) (2006);
  • T. Egami, Matsumoto, O., Yahiro, PTP 121, 789 (2009).
  • K. Minomo, O., Shimizu, Kohno, Yahiro, J Phys. G 37, 085011 (2010).
  • S. Hashimoto, O., Chiba, Yahiro, PTP 122, 1291 (2009);
  • T. Ye, Watanabe, O., Chiba, PRC78, 024611 (2008);
  • T. Ye, Watanabe, O., PRC80, 014604 (2009).
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Microscopic CDCC

 (Global) N-A and A-A optical potentials are necessary for systematic analysis with CDCC

A

n n p c

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 Localization of microscopic opt. pot.  Proper NN eff. int. in nuclear medium  “Predictability” and applicability

Microscopic optical potentials

  • T. Furumoto, Sakuragi, Yamamoto, PRC78, 044610 (2008);

79, 011601(R) (2009).

Key points

c.f. K. Amos et al., adv. Nucl. Phys. 25, 275 (2000).

p-90Zr at 65 MeV

  • K. Minomo, O., Shimizu, Kohno, Yahiro, JPG in press;

arXiv:0911.1184 c.f. F. A. Brieva and J. R. Rook, NP A291, 317 (1977).

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Nucleon-nucleus scattering

: ground-state wave function of the target

The equation for the relative motion Folding potential

  • F. A. Brieva and J. R. Rook, Nucl. Phys. A 291, 317 (1977).

□ Folding model We obtain the localized folding potential with the Brieva-Rook (BR) method.

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Structure model

 Hartree-Fock method with finite-range Gogny force It is applicable to obtain the ground-state wave function of all nuclei. The properties of many stable nuclei such as the binding energy are well reproduced. We find that this method is reliable.

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Interaction for reaction dynamics

 Melbourne g-matrix HF method with Gogny force Pure theoretical framework without any parameter Two-body interaction which depends on the target density □ The framework in this study Melbourne g-matrix BR localization

  • K. Amos, P. J. Dortmans, H. V. von Geramb, S. Karataglidis and J. Raynal,
  • Adv. Nucl. Phys. 25, 275 (2000).
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p +90Zr elastic scattering

Stable nucleus

90Zr

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Central (microscopic) + LS (Dirac phenomenology)

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6,8He+p elastic scattering

Unstable nucleus

6He

Unstable nucleus

8He

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The validity of BR localization

It is necessary to test the accuracy of the BR localization.

For only elastic scatterings, one can calculate the exact form. Exact: BR: We have to solve the Schrödinger equations We tested the validity of the BR localization by comparison of the exact calculation and BR calculation.

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Exact vs BR for p+90Zr

90Zr

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Exact vs BR for 6He+p and 8He+p

6He 8He

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No Perey factor needed!

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Application

□ For deuteron induced reaction three-body model Optical potentials as an input  Continuum-Discretized Coupled-Channels method (CDCC) It is a standard direct reaction theory to describe real and virtual breakup.

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d +58Ni elastic scattering

Success of Microscopic CDCC

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Microscopic CDCC for 6Li induced reactions

10 20 30 40 50 60 10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

208Pb at 210 MeV

10 20 30 40 50 60 10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 10

1

28Si at 240 MeV

10 20 30 40 50 60 10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

12C at 150 MeV

10 20 30 40 50 60 10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

40Ca at 210 MeV

cm (deg) cm (deg) Rutherford Ratio delas /d (mb/sr) delas /d (mb/sr) delas /d (mb/sr) (d++A model: d-A and -A potentials are evaluated with JLM eff. int. and HF densities.

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Outline

0) Brief introduction to CDCC 1) Four-body breakup processes for 6He induced reaction

  • M. Kamimura, Yahiro, Iseri, Sakuragi, Kameyama and Kawai, PTP Suppl. 89, 1 (1986);
  • N. Austern, Iseri, Kamimura, Kawai, Rawitscher and Yahiro, Phys. Rep. 154 (1987) 126.

2) Microscopic description of projectile breakup processes 3 New approach to inclusive breakup processes

  • T. Matsumoto, Hiyama, O., Iseri, Kamimura, Chiba, Yahiro, PRC70, 061601(R) (2004);
  • T. Matsumoto, Egami, O., Iseri, Kamimura, Yahiro, PRC73, 051602 (R) (2006);
  • T. Egami, Matsumoto, O., Yahiro, PTP 121, 789 (2009).
  • K. Minomo, O., Shimizu, Kohno, Yahiro, J Phys. G 37, 085011 (2010).
  • S. Hashimoto, O., Chiba, Yahiro, PTP 122, 1291 (2009);
  • T. Ye, Watanabe, O., Chiba, PRC78, 024611 (2008);
  • T. Ye, Watanabe, O., PRC80, 014604 (2009).
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Inclusive BU (incomplete fusion) process

7Li(d,nx) 7Li

n p ??? n p

7Li

Dividing the integration region with respect to absorbing radii of p and n. Total Fusion: p and n absorbed

  • nly p absorbed
  • nly n absorbed

no contribution

c.f. IFMIF project

  • S. Hashimoto, O., Chiba, Yahiro, PTP122, 1291 (2009).
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Determination of abs. rad.

 CDCC + Glauber reproduces the data.  Integrated stripping X-sec. calculated with Glauber model is assumed to be an exp. value.  Abs. Rad. are adjusted to reproduce this value. Key points

7Li(d,nx) at 40 MeV

  • T. Ye, Watanabe, O., PRC80, 014604 (2009).
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Inclusive BU (incomplete fusion) X-sec.

  • A. Diaz-Torres and I. J. Thompson, PRC65, 024606 (2002).

Key points  Inclusive BUX is very large.  and have opposite Ed dependence.  Previous method gives very different results. Future work  Calculation of inclusive triple diff. X-sec. (Eikonal Reaction Theory; ERT)

( ) IF p

( ) IF n

  • S. Hashimoto, O., Chiba, Yahiro, PTP122, 1291 (2009).
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Summary

1) Four-body breakup processes for 6He induced reaction 2) Microscopic description of projectile breakup processes 3) New approach to inclusive breakup processes

 Direct comparison with exp. data  Five- and Six-body CDCC using Cluster-Orbital Shell Model  Triple differential X-sec. of inclusive process  Application of microscopic opt. pot. to systematic CDCC calculations

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Collaborators

A,BTakuma Matsumoto, CShintaro Hashimoto, DKosho Minomo, EYasunori Iseri, FMichio Kohno, CSatoshi Chiba, DTaiga Hamada, DYoshifumi R. Shimizu, GYe Tao, GYukinobu Watanabe, and DMasanobu Yahiro ARIKEN Nishina Center BMeme Media Laboratory, Hokkaido University CJapan Atomic Energy Agency DDepartment of Physics, Kyushu University EChiba-Keizai College FKyushu Dental College GDepartment of Advanced Energy Engineering Science, Kyushu University