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Futoshi Minato JAEA Nuclear Data Center, Tokai Theoretical calculations of beta-delayed neutrons and sensitivity analyses 1
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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
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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
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4 1. DN Emission Probabilities by SHF+QRPA plus HFSM Calculations of DN Emission Probability β-β- Parent/ Precursor (Z,N) Daughter (Z+1,N-1) (Z+1,N-2) n g.s. γ
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5 1. DN Emission Probabilities by SHF+QRPA plus HFSM β-β- Parent/ Precursor (Z,N) Daughter (Z+1,N-1) (Z+1,N-2) n QRPA HFSM g.s. T 1/2 Strength Function P n (P 1n, P 2n, P 3n ) Neutron Spectrum γ Calculations of DN Emission Probability
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6 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 SkOSAMi Strength of Pairing (p,n) Odd Nuclei Skyrme Effective Force p or n core (330,323)(256,258) Valence Particle is assumed to follow Indep. Particle Model Blocking Effect in QRPA
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7 1. DN Emission Probabilities by SHF+QRPA plus HFSM QRPA Prescription to determine T=0 pairing strength V pp 1.Search appropriate V pp reproducing T 1/2 of E-E Nuclei 2.Calculate Average V pp ave (Z) from V pp of same Z 3.Calculate T 1/2 of isotope chains systematically with V pp ave (Z) SkO Atomic Number Z Isospin T=0 pairing Attractive in GT channel Strong pairing Low 1+ state in daughter Shorter T 1/2 V pp (Z) Daughter g.s. 1+
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8 1. DN Emission Probabilities by SHF+QRPA plus HFSM 233 nuclei rms=5.09 T 1/2 (calc) / T 1/2 (exp) SKO
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9 1. DN Emission Probabilities by SHF+QRPA plus HFSM HF Hauser-Feshbach Models implemented in the nuclear reaction calculation code, “CCONE”. Neutron Transmission Coefficient : Koning-Delaloche Optical Pot. Gamma-ray Transmission Coefficient : Kopecky-Uhl’s EGLO Level-Density: Fermi Gas Model with Mengoni-Nakajima parameter set at high excitation energy (Z+1,N-2) n g.s. Daughter (Z+1,N-1) γ n γ β-β- Parent (Z,N) Q β =1.SHF+BCS 2.Experiment
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DN Emission Prob. for Z=35-44 (Q β : SHF+BCS) 10 1. DN Emission Probabilities by SHF+QRPA plus HFSM SKO
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11 1. DN Emission Probabilities by SHF+QRPA plus HFSM DN Emission Prob. for Z=27-30 (Q β : exp. or KTUY)
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12 1. DN Emission Probabilities by SHF+QRPA plus HFSM P2n & P3n (Q β : exp. or KTUY) A (Co isotopes) P2n or P3n SAMi(P2n) SkO(P2n) SAMi(P3n) SkO(P3n)
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13 DN Spectra 1. DN Emission Probabilities by SHF+QRPA plus HFSM Cu-81 Zn-83 g.s. Daughter (Z+1,N-1) β-β- Parent (Z,N) φ n (MeV -1 )/ 1 fission E (MeV)
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14 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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15 2. Incident Neutron Energy Dependence of Delayed Neutron Yields Energy Dependence of DN Yields in Nuclear Data
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16 Fission Yield Data Decay Data Activity 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 Equation Energy Dependent 137 Te 137 I 137 Xe 137 Cs 137 Ba 137m Ba 炉物理の研究 第 64 号( 2012 年 3 月)吉田先生 β-β- β-β- β-β- β-β- β-β- 0.4% 0.1% 3.2% 2.7% Indep. FY 2.6m IT 2.5s24.5s 3.8m 30.1y βn=2.9%βn=7.1%
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17 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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18 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 Yield/fission
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19 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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20 Sensitivity Test Fission Yields DN Emission Prob. 3. Sensitivity Analysis of Delayed Neutron with JENDL
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235 U: 86 Ge, 89 Br, 90 Br, 94 Rb, 137 I Thermal Neutron Fission 239 Pu: 89 Br, 90 Br, 94 Rb, 98m Y, 137 I, 138 I Remarkable Nuclei 235 U: 86 As, 88 Br, 89 Br, 90 Br, 94 Rb, 137 I 239 Pu: 88 Br, 89 Br, 90 Br, 94 Rb, 98m Y, 137 I, 138 I 21 3. Sensitivity Analysis of Delayed Neutron with JENDL
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Nucl. Yield error Err./Yield Ge-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./Pn Ge-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-2011 Indep. Fission Yields Pn(%) Red represents uncertainty > 5% 22 3. Sensitivity Analysis of Delayed Neutron with JENDL
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23 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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24 4. Important Precursors in r-process Nucleosynthesis 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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25 4. Important Precursors in r-process Nucleosynthesis 1. Ag-129 4.79E-01 2. Rh-127 1.54E-01 3. Pd-128 7.33E-02 4. Cd-130 6.16E-02 5. Rh-125 5.59E-02 6. In-131 2.76E-02 7. Ru-126 1.68E-02 8. Pd-126 1.67E-02 9. Al-35 1.64E-02 10. Nb-109 1.56E-02 1. Sb-137 9.63E-02 2. Sb-135 8.06E-02 3. Ag-129 6.75E-02 4. P-41 6.72E-02 5. I-141 6.27E-02 6. Cl-46 5.67E-02 7. Cd-130 4.12E-02 8. Sn-136 3.14E-02 9. I-143 3.07E-02 10. 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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26 4. Important Precursors in r-process Nucleosynthesis 1. Sb-137 1.28E-01 2. Cl-46 7.14E-02 3. P-41 7.12E-02 4. Sb-135 6.29E-02 5. I-143 3.10E-02 6. I-141 2.99E-02 7. Sn-136 2.43E-02 8. La-157 2.41E-02 9. Pr-161 2.08E-02 10. La-155 1.93E-02 Ye=0.3, τ=16.6ms, s/k=205
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27 Thank you for you attention
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