gamow-teller transitions for light nuclei by the deformed quasi-particle rpa(dqrpa)

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Gamow-Teller Transitions for Light Gamow-Teller Transitions for Light Nuclei Nuclei by the by the Deformed Quasi-particle Deformed Quasi-particle RPA(DQRPA) RPA(DQRPA) Soongsil University, Korea Eun Ja HA and Myung-Ki CHEOUN Eun Ja HA and Myung-Ki CHEOUN 1 2011 HNP

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Gamow-Teller Transitions for Light Nuclei by the Deformed Quasi-particle RPA(DQRPA). Soongsil University, Korea Eun Ja HA and Myung-Ki CHEOUN. Contents. Motivation Formalism - Deformed basis (Nilsson basis) - Deformed Bardeen Cooper Schrieffer (DBCS) - PowerPoint PPT Presentation

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Page 1: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Gamow-Teller Transitions for Light Nuclei Gamow-Teller Transitions for Light Nuclei by the by the Deformed Quasi-particle Deformed Quasi-particle

RPA(DQRPA)RPA(DQRPA)

Soongsil University, KoreaEun Ja HA and Myung-Ki CHEOUNEun Ja HA and Myung-Ki CHEOUN

12011 HNP

Page 2: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

ContentsContents

• Motivation • Formalism

- Deformed basis (Nilsson basis) - Deformed Bardeen Cooper Schrieffer (DBCS)- Deformed quasi-particle random phase approximation (DQRPA) - Gamow-Teller transitions for the nuclear beta decay

• Results• Summary

22011 HNP

Page 3: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

23年 4月 22日 SKKU, 17 June. 2010 31

Motivations

Formalism Results Summary

X-ray and Super Burst

~ 3hours

Time scaleTime scale : ~ : ~ a few hoursa few hours Total energy : 10Total energy : 104242 erg (normal burst ~ 10 erg (normal burst ~ 103939 erg)erg)

Supernovae Type II

32011 HNP

Page 4: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

23年 4月 22日 SKKU, 17 June. 2010 414

Pycno‐reaction (Haensel & ZdunikPycno‐reaction (Haensel & Zdunik1990 )1990 )Because of high density and low temperature on the

neutron star crust, Coulomb barrier is overcome by the zero-point motion of the nuclei in the

solid lattice !!

Degenerated electrons block the beta decay. Ordinary nuclei become highly unstable, and unstable nuclei become the normal stable nuclei at the neutron-star crusts !!

4

Motivations

Formalism Results Summary

2011 HNP

Page 5: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

5

spherical basis deformation np-pairing correlation

proton neutron

Motivations

Formalism Results Summary

☞ The conventional approach so far to understand the nuclear structure is based on the spherical symmetry.

2011 HNP

Page 6: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

6

We extend our previous QRPA based on the spherical symmetry, which turns out to be a very useful tool for relevant reactions in the nuclear-astrophysics.

Motivations

Formalism Results Summary

2011 HNP

Page 7: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Realistic two body interaction

taken by Brueckner G-matrix

based on the Bonn potential

Deformed WS

Deformed BCS

Deformed QRPA

Gamow-Teller transition

7

Without np-pairingWith np-pairing(in progress)

Motivations

Results Summary Formalism

FormalismFormalism

2011 HNP

Page 8: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

• The single particle states

)p,n(nNb z

zNn

zNn

8

Spin w.f

Axially symmetric harmonic oscillator w.f.

Motivations

Results Summary Formalism

2011 HNP

Page 9: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

• The deformed basis(Nilsson basis) is expanded

9

zNn

rn0N

zNnj

21

)(j0N

r

a

)(a

bACB,where

ljnaaB

)jN(

'00)jN( J

)JK(jj

)'()jN(

)()jN('

0 '0

'''00JK,)jN()jN(CBB'

'n0'p0n0p0JK

jjJK

jj

)jN( )jN( )jN( )jN(

)'n()jN(

)'p()jN(

)n()jN(

)p()jN(

J'n'pnp

)jN()jN(G)jN()jN(CC

BBBB'n'pGnp

'n'n'p'pnnpp

p0 n0 'p0 'n0

'n0'p0n0p0

Spherical harmonic oscillator w. f.

Motivations

Results Summary Formalism

By Including deformation

2011 HNP

Page 10: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Deformed BCSDeformed BCS In order to renormalize the G-matrix, theoretical values are adjusted to the empirical pairing potentials by multiplying the G-matrix with a strength parameters gpp(gnn).

10

Motivations

Results Summary Formalism

By Including deformation

by a symmetric five term formula

2011 HNP

Page 11: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Description of Intermediate States for Gamow-Teller excitation K=1,0,-1

stategroundQRPA:rpawhererpaQm),K(1 K,m

11

Motivations

Results Summary Formalism

DQRPA equation

2011 HNP

Page 12: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

12

particle-hole

particle-particle

Motivations

Results Summary Formalism

Realistic two body interaction taken by Brueckner G-matrix

based on the Bonn potential

By Including deformation

2011 HNP

Page 13: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Beta- transition amplitude

13

Motivations

Results Summary Formalism

2011 HNP

Page 14: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

14

Results Formalism Summary Motivations

Results Summary Formalism

Ikeda sum rulein percentage of

3(N-Z)

2011 HNP

Page 15: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

15

Gamow-Teller Strength in 26Mg

Results Formalism Summary Motivations

Results Summary Formalism

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

0

1

2

3

4

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 90

1

2

3

4

0

1

2

3

4

5

(e) 2= -0.25

B(G

T- )B

(GT- )

(b) 2= 0.1

Eex

[MeV]

(d) 2= -0.1

Eex

[MeV]

B(G

T- )

(c) 2= 0.25

[ 8 < Eex

< 13.3 ]

(a) 26Mg (p,n)26Al

[ 0 < Eex

< 8 ]

Experimentby Madey

(1987)

2011 HNP

Page 16: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

16

-1 0 1 2 3 4 5 6 7 80

1

2

3

4

0

1

2

3

4

0

1

2

3

4

5

(c) 2= - 0.1

(b) 2= 0.25

B(G

T)

B(G

T)

(a) 2= 0.1

B(G

T)

Ex[MeV]

Gamow-Teller Strength in 60Ni

Results Formalism Summary Motivations

Results Summary Formalism

Experiment

Ours60Ni (p,n)

60Cu

60Ni (n,p) 60Co

2011 HNP

Page 17: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

17

Gamow-Teller strength in 76Ge Experime

nt

Results Formalism Summary Motivations

Results Summary Formalism

0

5

10

15

20

0 5 10 15 200

5

10

15

0 5 10 15 20

(a) 2= 0.1

B(G

T - )

Ex[MeV]

(b) 2= 0.25

Ex[MeV]

B(G

T - )

(c) 2= -0.1

(d) 2= -0.25

Calculatiion by Fedor.

2011 HNP

Page 18: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

18

1. To describe a single particle state in deformed basis, we

used the deformed axially symmetric Woods-Saxon potential.

And then we performed the deformed BCS and deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn potential.

2. We calculated the Gamow-Teller transitions in 26Mg , 60Ni, and 76Ge. Our results are reproduced well the position of energy with available experimental data and other calculations but we have some problem for the B(GT) strength.

3. We are checking transition operator and np-pairing correlations to improve the B(GT) strength.

Motivations

Formalism Results Summary

Summary

2011 HNP

Page 19: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

19

1. Next stage is E1 and E2 transitions in unstable nuclei to study the inversion island, which comes from the shell evolution sensitive to the deformation .

2. Weak interactions with unstable nuclei by the neutrino, in specific, stemmed from the supernova explosion are also one of the interesting topics, because relevant cross sections are believed to differ from those in stable nuclei and affect rapid processes in the nucleosynthesis on the corecollapsing supernovae and/or the crust of the neutron star with a binary star.

Future works

2011 HNP

Page 20: Gamow-Teller Transitions for Light Nuclei  by the  Deformed Quasi-particle RPA(DQRPA)

Thanks for your attention !!Thanks for your attention !!

202011 HNP