futoshi minato jaea nuclear data center, tokai theoretical calculations of beta-delayed neutrons and...
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Futoshi Minato
JAEA Nuclear Data Center, Tokai
Theoretical calculations of beta-delayed neutrons and
sensitivity analyses
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2
1. Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model (HFSM)
2. Incident Neutron Energy Dependence of DN Yields
3. Sensitivity Analysis of DN with JENDL evaluated libraries
4. Important Precursors in r-process Nucleosynthesis
Contents of This Talk
3
1. Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model
2. Incident Neutron Energy Dependence of DN Yields
3. Sensitivity Analysis of DN with JENDL evaluated libraries
4. Important Precursors in r-process Nucleosynthesis
Contents of This Talk
4
1. DN Emission Probabilities by SHF+QRPA plus HFSM
Calculations of DN Emission Probability
β-
Parent/Precursor
(Z,N)
Daughter(Z+1,N-1)
(Z+1,N-2)
ng.s.
g.s.
g.s.
γ
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
β-
Parent/Precursor
(Z,N)
Daughter(Z+1,N-1)
(Z+1,N-2)
n
QRPA HFSM
g.s.
g.s.
g.s.
T1/2
Strength FunctionPn (P1n, P2n, P3n)
Neutron Spectrum
γ
Calculations of DN Emission Probability
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
QRPA •On top of Skyrme-Hartree-Fock+BCS•Deformation (cylind. coordinate space)•Volume-type Pairing force in BCS•Residual Interaction : Same as G.S. Include All Terms self-consistently
SkO SAMiStrength of Pairing (p,n)
Odd Nuclei
Skyrme Effective Force
p or ncore
(330,323)(256,258)
Valence Particle is assumed to follow Indep. Particle Model
Blocking Effect in QRPA
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
QRPA
Prescription to determine T=0 pairing strength Vpp1. Search appropriate Vpp reproducing T1/2 of E-E Nuclei2. Calculate Average Vpp
ave(Z) from Vpp of same Z3. Calculate T1/2 of isotope chains systematically with Vpp
ave(Z)
SkO
Atomic Number Z
Isospin T=0 pairing Attractive in GT channelStrong pairing Low 1+ state in daughter Shorter T1/2
V pp(Z
)
Daughterg.s.
1+
1+
1+
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
233 nucleirms=5.09
T 1/2(c
alc)
/ T 1/
2(exp
) SKO
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
HF Hauser-Feshbach Models implemented in the nuclearreaction calculation code, “CCONE”.
Neutron Transmission Coefficient : Koning-Delaloche Optical Pot.Gamma-ray Transmission Coefficient : Kopecky-Uhl’s EGLOLevel-Density: Fermi Gas Model with Mengoni-Nakajima parameter set at high excitation energy
(Z+1,N-2)
n
g.s.
g.s.
Daughter(Z+1,N-1)
γn
γ
β-
Parent(Z,N)
Qβ=1.SHF+BCS 2.Experiment
DN Emission Prob. for Z=35-44 (Qβ : SHF+BCS)
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
SKO
SKO
SKO
SKO
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
DN Emission Prob. for Z=27-30 (Qβ : exp. or KTUY)
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1. DN Emission Probabilities by SHF+QRPA plus HFSM
P2n & P3n (Qβ : exp. or KTUY)
A (Co isotopes)
P2n
or P
3n
SAMi(P2n)
SkO(P2n)SAMi(P3n)
SkO(P3n)
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DN Spectra
1. DN Emission Probabilities by SHF+QRPA plus HFSM
Cu-81Zn-83
g.s.Daughter(Z+1,N-1)
β-
Parent(Z,N)
φn (
MeV
-1)/
1 fi
ssio
n
E (MeV) E (MeV)
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1. Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model
2. Incident Neutron Energy Dependence of DN Yields
3. Sensitivity Analysis of DN with JENDL
4. Important Precursors in r-process Nucleosynthesis
Contents of This Talk
15
2. Incident Neutron Energy Dependence of Delayed Neutron Yields
Energy Dependence of DN Yields in Nuclear Data𝜈𝑡𝑜𝑡
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𝜈𝑡𝑜𝑡=∫𝜈𝑑(𝑡)𝑑𝑡𝜈𝑑(𝑡)=∑
𝑖
𝜆𝑃𝑛(𝑖)𝑦 𝑖(𝑡) Fission Yield Data
Decay DataActivity of DN
DN Yield
2. Incident Neutron Energy Dependence of Delayed Neutron Yields
Detail can be found in [2].Calculation is performed with Code [3].
Bateman Equation𝑑𝑛1(𝑡)𝑑𝑡
=− 𝜆1𝑛1(𝑡)
𝑑𝑛𝑘(𝑡)𝑑𝑡
=− 𝜆𝑘𝑛𝑘 (𝑡 )+𝜆𝑘−1𝑛𝑘−1 (𝑡 )(2≤𝑘)
𝑛𝑖 (𝑡 )=𝑦 𝑖∑𝑗=1
𝑖
𝑑 𝑗𝑒−𝜆 𝑗 𝑡
𝑑 𝑗=1 (𝑖= 𝑗=1 )
𝑑 𝑗=∏𝑘=1
𝑖−1
𝜆𝑘
∏𝑘=1 ,𝑘≠ 𝑗
𝑗
(𝜆¿¿𝑘−𝜆 𝑗)(2≤ 𝑗≤ 𝑖 ) ¿
Energy Dependent
137Te 137I 137Xe 137Cs 137Ba
137mBa
炉物理の研究 第 64 号( 2012 年 3 月)吉田先生
β- β- β- β-
β-0.4% 0.1%3.2%2.7%
Indep. FY
2.6m IT
2.5s 24.5s 3.8m 30.1yβn=2.9% βn=7.1%
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2. Incident Neutron Energy Dependence of Delayed Neutron Yields
Decay Data : JENDL/FPD-2011 J. Katakura, JAEA-DATA/Code2011-025(2011)
Bad Reproduction
Fission Yields : 5 Gaussian Model
1. Mass Distribution & Prompt Neutron: J. Katakura, JAERI-Research2003-004(2003)2. Charge Distribution: T.F. England and B.F.Rider, LA-UR-94-3106,ENDF-349(1994).3. Isomer states: J. Katakura, JAEA-DATA/Code2011-025(2011)
Wahl, IAEA-TECDOC-1168(2000)
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2. Incident Neutron Energy Dependence of Delayed Neutron Yields
Correction in A) D.R. Nethaway, Lawrence Livermore Laboratory Report No. UCRL-51538, (1974). (see also D.R. Alexander and M.S. Krick, Nucl. Sci. Eng. 62, 627 (1977) )B) V.A. Roshchenko, V.M. Piksaikin et al., Phys. Rev. C74, 014607 (2006)
Energy Dependence of charge distribution:
E (eV)
DN
Yie
ld/fi
ssio
n
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1. Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model
2. Incident Neutron Energy Dependence of DN Yields
3. Sensitivity Analysis of DN with JENDL
4. Important Precursors in r-process Nucleosynthesis
Contents of This Talk
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𝑆𝑌 𝑖=
(∆𝜈¿¿𝑑¿𝜈𝑑)(∆𝑌 𝑖/𝑌 𝑖)
¿
𝑆𝑃 𝑛𝑖=
(∆𝜈 ¿¿𝑑 ¿𝜈𝑑)(∆ 𝑃𝑛𝑖 /𝑃𝑛𝑖)
¿
Sensitivity Test
Fission Yields
DN Emission Prob.
3. Sensitivity Analysis of Delayed Neutron with JENDL
Δ 𝑦 𝑖 /𝑦 𝑖=¿ Δ 𝑃𝑛(𝑖)/𝑃𝑛 (𝑖 )=0.1¿
235U: 86Ge,89Br,90Br,94Rb, 137I
𝑆 𝑦 𝑖
𝑆𝑃 𝑛(𝑖)
Thermal Neutron Fission
239Pu: 89Br,90Br,94Rb,98mY,137I,138I
Remarkable Nuclei
235U: 86As, 88Br,89Br,90Br,94Rb, 137I
239Pu: 88Br,89Br,90Br,94Rb,98mY,137I,138I
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3. Sensitivity Analysis of Delayed Neutron with JENDL
Nucl. Yield error Err./YieldGe-86 0.6278 0.1005 (16%)As-85 0.1212 0.0775 (63%)As-86 0.0199 0.0127 (64%)Br-89 1.0379 0.0415 (4%)Br-90 0.5518 0.0331 (6%)Rb-94 1.5644 0.0438 (2.8%)Y-98m 1.8739 0.5996 (32%)Sb-135 0.1449 0.0116 (8%)Te-137 0.3919 0.0313 (8%)Te-138 0.0661 0.0423 (64%)I-137 2.6189 0.1048 (4%)I-138 1.4222 0.0398 (2.8%)
Nucl Pn(%) err. err./PnGe-86 6 N/A (----)As-85 59.4 29 (48.8%)As-86 33.0 4.0 (12%)Br-89 13.8 0.4 (2.9%)Br-90 25.2 0.9 (3.6%)Rb-94 10.5 0.4 (3.8%)Y-98m 3.4 1.0 (29%)Sb-135 22 3 (13.6%)Te-137 2.99 0.16 (5.4%)Te-138 6.3 2.1 (33%)I-137 7.14 0.23 (3.22%)I-138 5.56 0.22 (3.96%)
Uncertainties in JENDL/FPY & FPD-2011Indep. Fission Yields Pn(%)
Red represents uncertainty > 5% 22
3. Sensitivity Analysis of Delayed Neutron with JENDL
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1. Delayed Neutron (DN) Emission Probabilities by Skyrme-HF+QRPA plus Hauser-Feshbach Statistical Model
2. Incident Neutron Energy Dependence of DN Yields
3. Sensitivity Analysis of DN with JENDL
4. Important Precursors in r-process Nucleosynthesis
Contents of This Talk
24
4. Important Precursors in r-process Nucleosynthesis
𝑆=∫𝑡 𝑓 .𝑜 .
∞
𝑃𝜈(𝑖)𝑌 𝑖
∑𝑖∫𝑡 𝑓 . 𝑜 .
∞
𝑃𝜈 (𝑖)𝑌 𝑖
This Work is performed with T. Kajino & Shibagaki at NAOJ
Important DN precursor after freeze-out(f.o.) in r-process
We define
Tells information which nucleus emits neutron efficiently after f.o.
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4. Important Precursors in r-process Nucleosynthesis
1. Ag-129 4.79E-012. Rh-127 1.54E-013. Pd-128 7.33E-024. Cd-130 6.16E-025. Rh-125 5.59E-026. In-131 2.76E-027. Ru-126 1.68E-028. Pd-126 1.67E-029. Al-35 1.64E-0210. Nb-109 1.56E-021. Sb-137 9.63E-022. Sb-135 8.06E-023. Ag-129 6.75E-024. P-41 6.72E-025. I-141 6.27E-026. Cl-46 5.67E-027. Cd-130 4.12E-028. Sn-136 3.14E-029. I-143 3.07E-0210. Sn-134 2.76E-02
Ye=0.3, τ=16.6ms, s/k=105
Ye=0.3, τ=16.6ms, s/k=155
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4. Important Precursors in r-process Nucleosynthesis
1. Sb-137 1.28E-012. Cl-46 7.14E-023. P-41 7.12E-024. Sb-135 6.29E-025. I-143 3.10E-026. I-141 2.99E-027. Sn-136 2.43E-028. La-157 2.41E-029. Pr-161 2.08E-0210. La-155 1.93E-02
Ye=0.3, τ=16.6ms, s/k=205
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Thank you for you attention