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ガンマ線強度関数法によるアプローチ. Approach by the g -ray strength function method. H. Utsunomiya (Konan University) Outline Methodology of the g SF method Applications to unstable nuclei along the valley of b -stability comments on a versatile application based on Coulomb dissociation experiments.

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ガンマ線強度関数法によるアプローチ

Approach by the g-ray strength function method

H. Utsunomiya (Konan University)

Outline

  • Methodology of the gSF method

  • Applications to unstable nuclei along the valley of b-stability

  • comments on a versatile application based on Coulomb dissociation experiments

2011年度核データ研究会プログラム

2011年11月16日(水) – 17日(木)

日本原子力研究開発機構テクノ交流館リコッティ


Collaborators

H. Utsunomiyaa) , H. Akimunea) , T. Yamagataa) , H. Toyokawac) , H. Haradad), F. Kitatanid) ,

Y. -W. Luie) ,

S. Gorielyb)

I. Daoutidisb) , D. P. Arteagaf) ,

S. Hilaireg) , and A. J. Koningh)

  • Department of Physics, Konan University, Japan

  • Institut d’Astronomie et d’Astrophysique, ULB, Belgium

  • c) National Institute of Advanced Industrial Science and Technology, Japan

  • d) Japan Atomic Energy Agency, Tokai, Naka-gun, Ibaraki 319-1195, Japan

  • e) Cyclotron Institute, Texas A&M University, USA

  • f) Institut de Physique Nucléaire, Université Paris-Sud, France

  • g) CEA,DAM, DIF, Arpajon, France

  • h) Nuclear Research and Consultancy Group, The Netherlands


Radiative neutron capture cross sectionsfor unstable nuclei in nuclear engineering and nuclear astrophysics

Direct measurements at CERN n-TOF, LANSCE-DANCE, Frankfurt-FRANZ and J-Parc ANNRI facilities

can target some of unstable nuclei along the valley of b-stability if samples can be prepared. ---> s-process

Indirect experimental method is called in

for unstable nuclei

along the valley of b-stability ---> s-process,

neutron-rich region ---> r-process

surrogate reaction technique

ANY OTHER?


G ray strength function method
g-ray strength function method

H. Utsunomiya et al., PRC80 (2009)

follows the statistical model of the radiative neuron capture in the formation of a compound nucleus and its decay by using experimentally-constrained gSF.

Radiative neutron capture

AX(n,g)A+1X

continuum

E, J, p

decay process

gSF

NLD

n + AX

A+1X


Hauser-Feshbach model cross section for AX(n,g)A+1X

Total gtransmission coefficient

After integrating over J and π

nuclear level density

g-ray strength function

X=E, M

l=1, 2, …

neutron resonance spacing

low-lying levels

source of uncertainty

gSF method


g-ray strength function: nuclear statistical quantity interconnecting (n,g) and (g,n) cross sectionsin the HF model calculation

Radiative neutron capture

Photoneutron emission

continuum

AX(n,g)A+1X

A+1X(g,n)AX

E, J, p

n+AX

A+1X

Brink Hypothesis


Structure of g ray strength function
Structure of g-ray strength function

Extra strengths

Sn

GDR

6 – 10 MeV

PDR, M1

Primary strength

E1 strength in the low- energy tail of GDR


Methodology of gSF method

STEP 1

GDR

(g,n)

Measurements of (g,n) c.s. near Sn

STEP 1

gSF

(g,n)

A-1

A

Sn


Methodology of gSF method

STEP 2

GDR

(g,n)

Normalization of gSF

Extrapolation of gSF

by models

STEP 1

gSF

(g,n)

A-1

A

Sn

Sn


Methodology of gSF method

STEP 2

GDR

(g,n)

JUSTIFICATION BY REPRODUCING KNOWN

(n,g) C.S.

STEP 1

gSF

(g,n)

A-1

A

Sn

Sn

known (n,g)


Methodology of gSF method

STEP 3

GDR

(g,n)

neutron capture by

unstable nucleus

A+1X(n,g)A+2X

STEP 1

STEP 2

STEP 1

STEP 2

gSF

(g,n)

(g,n)

A-1

A

A+1

A+2

Extrapolation is made in

the same way as for stable

isotopes.

Sn

STEP 3

known (n,g)

(n,g) to be determined


Applications

LLFP (long lived fission products)

nuclear waste

Astrophysical significance

Present (g,n) measurements

Existing (n,g) data

H. Utsunomiya et al., PRC80 (2009)

(n,g) c.s. to be deduced

121

27 h

123

129 d

6

6

Sn

117

116

118

119

120

122

124

115

7

H.U. et al., PRC82 (2010)

107

6.5 106 y

3

106

108

Pd

105

104

H.U. et al., PRL100(2008)

PRC81 (2010)

93

1.53 106 y

95

64 d

5

89

3.27 d

Zr

94

90

91

92

96

79

2.95 103 y

To be published

F. Kitatani et al.

75

120 d

Se

78

80

76

77

4


Laser Compton scattering g-ray beam

Inverse Compton Scattering

“photon accelerator”

g = Ee/mc2



Detector System Technology)

Triple-ring neutron detector

20 3He counters (4 x 8 x 8 ) embedded in polyethylene


Applications Technology)

H. Utsunomiya et al., PRC, in press (2011)

H. Utsunomiya et al., PRC80 (2009)

121

27 h

123

129 d

6

6

Sn

117

116

118

119

120

122

124

115

7


Sn Technology) isotopes

STEP 1 Measurement of (g,n) cross sections


STEP 2 Technology)– Extrapolation of gSF to the low-energy region

HFB+QRPA

+ PDR

HFB+QRPA E1 strength supplemented with a pygmy E1 resonance in Gaussian shape

Eo ~ 8.5 MeV, G ~ 2.0 MeV, so ~ 7 mb

~ 1% of TRK sum rule of GDR


STEP 2 Technology)– Justification of the extrapolated gSF


STEP 3 Technology)– Statistical model calculations of (n,g) cross sections for radioactive nuclei

Uncertainties:

30-40%

121Sn[T1/2=27 h]

123Sn[T1/2=129 d]

Uncertainties:

a factor of 3


Results for Zr isotopes Technology)

long-lived fission product

nuclear waste

93Zr[T1/2=1.5×106 y]


95 Technology)Zr[T1/2=64 d]

s-process branching

30-40% uncertainties


long-lived fission product Technology)

nuclear waste

107Pd[T1/2=6.5×106 y]

30-40% uncertainties stem from NLD


Coulomb dissociation in the g sf method
Coulomb dissociation in the Technology)gSF method

s-process branching nucleus

(g,n) by Coulomb dissociation

A

A+1

(n,g) to be determined by gSF method


S process branching nuclei
s-process branching nuclei Technology)

F. Käppeler et al., Rev. Mod. Phys. 83, 157 (2011)


Coulomb dissociation experiments
Coulomb dissociation experiments Technology)

F. Käppeler et al., Rev. Mod. Phys. 83, 157 (2011)

18 Coulomb dissociations

11 branching nuclei


Ambitious application of the g sf method to the r process
Ambitious application of the Technology)gSF method to the r-process

131Sn(n,g)132Sn cross sections in the r-process nucleosynthesis

The astrophysical significance is controversial!

BUT this would be the first application to a very neutron-rich nucleus.

A pioneering work is in progress.

1) A systematic study of the gSF for Sn isotopes

116Sn ,…., 124Sn (7 stable) →→→ 132Sn

132Sn(g,n) data: GSI Coulomb dissociation data for 132Sn


Summary
Summary Technology)

gSF method: (n,g) c.s. for unstable nuclei

1. Nuclear Physics Experiment: (g,n) c.s. measurements

real photons for stable nuclei

virtual photons for unstable nuclei (CD)

2. Nuclear Theory:

models of gSF models of NLD

primary strength: low-energy E1 of GDR

extra strengths: PDR, M1

3. Coulomb dissociation experiments play a key role in a versatile application of the gSF method.

SAMURAI + NEBURA @ RIKEN-RIBF

ALADIN + LAND @GSI


Determination of (n, Technology)g) CS for unstable nuclei

原子力核データ、宇宙核物理(s-process)

along the valley of b-stability

宇宙核物理

r-process

p-process

far from stability

直接測定

Neutron beam

(n,g)

(g,n)

(g,n)

Photon beam

RI beam

ガンマ線強度関数法


Comparison with the surrogate reaction technique
Comparison with the surrogate reaction technique Technology)

Forssèn et al., PRC75, 055807 (2007)

Zr isotopes

93Zr(n,g)94Zr

95Zr(n,g)96Zr

1. The surrogate reaction technique gives larger cross sections by a factor of ~ 3 than the gSF method.

The surrogate reaction technique gives similar cross sections to those given by the gSF method provided that a choice is made of the Lorentian type of gSF.


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