Analysis of Reactor Beta- and Anti-Neutrino Energy Spectra on the basis of Gross Theory Tadashi Yoshida Tokyo Institute of Technology IAEA/NDS TAGS Meeting Vienna, Dec. 15-17, 2014 Aggregate e- & n-e Spectrum Calculations All the following calculations were performed based on the data files below along with the Gross Theory of Beta Decay (GT2) 1) Fission Yields: JENDL FP Yield Data File 2011 2) Decay Chains and Branchings: JENDL FP Decay Data File 2011 3) Beta and Neutrino Spectra: Gross Theory generation 2 (GT2) S.Chiba, T.Yoshida, T.Tachibana, N.Hagura, Proc. AESJ Fall Mtg., (2014) L55, Kyoto Electron Energy (MeV) Fig. Comparison between Measured and Calculated U-235 Electron Spectra (Calculated with Summation Method fully based on the Gross Theory) T.Tachibana, S.Chiba, T.Yoshida, N.Hagura, Proc. AESJ Fall Mtg., (2014) L56, Kyoto Neutrino Energy (MeV) Fig. Comparison between Measured and Calculated U-235 Neutrino Spectra (Calculated with Summation Method fully based on the Gross Theory) Neutrino Energy (MeV) Fig. Q-Value-wise FP Contributions to U-235 Electron Spectra (Calculated with Summation Method fully based on the Gross Theory) Fractional Contribution (cumulative) 1.00 0.90 0.80 8 MeV 0.70 6 MeV 0.60 4 MeV 0.50 2 MeV 0.40 0.30 0.20 0.10 0.00 0 10 20 30 40 50 Number of Contributing FPs Fig. Number of Contributors to U-235 Neutrino Spectra at 2 ~ 8 MeV Fractional Contribution (cumulative) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 Number of Contributing FPs Fig. Number of Contributors to U-235 Neutrino Spectra at 4MeV 200 Table FPs Contributing to Neutrino Spectrum from U-235 at 4MeV (These Top 30 Nuclides Cover 56% of the Total ) ZA 39094 37091 37092 38095 41098 36089 39095 55138 41100 38096 54139 57142 41101 53134 37093 55141 43102 39096 37089 37088 57144 37090 55139 40101 36091 40099 41102 56143 39097 54137 Nuclide Y-94 Rb-91 Rb-92 Sr-95 Nb-98 Kr-89 Y-95 Cs-138 Nb-100 Sr-96 Xe-139 La-142 Nb-101 I-134 Rb-93 Cs-141 Tc-102 Y-96 Rb-89 Rb-88 La-144 Rb-90 Cs-139 Zr-101 Kr-91 Zr-99 Nb-102 Ba-143 Y-97m Xe-137 Q (MeV) P-Index Hal-life 4.92 18.7 m 5.91 58.4 s 8.09 0.09-0.24 4.49 s 6.09 23.9 s 4.59 0.11 2.86 s 5.18 0.09 3.15 m 4.45 10.3 m 5.38 33.4 m 6.25 0.59 1.5 s 5.41 0.63 1.07 s 5.06 0.16 39.7 s 4.50 1.52 h 4.57 7.1 s 4.05 0.16 52.5 m 7.47 5.84 s 5.25 24.8 s 4.53 5.28 s 7.10 0.12 5.34 s 4.50 15.2 m 5.31 0.09 17.8 m 5.54 40.8 s 6.58 2.63 m 4.21 9.27 m 5.77 0.61 2.3 s 6.77 0.31 8.57 s 4.70 0.50 2.1 s 7.21 0.66 4.2 s 4.25 14.5 s 7.36 0.44 1.17 s 4.17 0.05 3.82 m Contribution 1.09E-03 1.06E-03 9.53E-04 9.05E-04 8.60E-04 7.86E-04 7.59E-04 7.45E-04 7.24E-04 7.19E-04 6.81E-04 6.78E-04 6.59E-04 6.50E-04 6.45E-04 6.12E-04 6.07E-04 5.96E-04 5.91E-04 5.86E-04 5.43E-04 5.32E-04 5.32E-04 5.24E-04 5.24E-04 5.05E-04 4.97E-04 4.70E-04 4.68E-04 4.58E-04 P-Index = (Q-Emax)/Q Q-Emax Q Emax Green: Idaho TAGS Blue: Jyvaskyla TAGS Red: Jyvaskyla IEEE(2013) Brown: On Request List in INDC(NDA)-0551 Pandemonity Index (P-Index) 0.7 0.6 Just for an Eye Guide 0.5 0.4 0.3 0.2 0.1 0 0.1 1 10 100 1000 Half-Life (second) Fig. Correlation Half-Life and P-Index of FP Nuclides Contributing to the Neutrino Spectrum at 4MeV Table FPs Contributing to Neutrino Spectrum from U-235 at 4MeV Cont’d 30~60 (Top 60 Nuclides Cover 83% of the Total ) ZA 55142 52135 55140 53137 39096 39097 36090 39099 36092 39098 35087 41103 35088 53136 35086 38093 59146 53136 37094 38097 43104 57145 40102 56145 53138 39098 52136 34086 40099 51132 Nuclide Cs-142 Te-135 Cs-140 I-137 Y-96 Y-97 Kr-90 Y-99 Kr-92 Y-98m Br-87 Nb-103 Br-88 I-136m Br-86 Sr-93 Pr-146 I-136 Rb-94 Sr-97 Tc-104 La-145 Zr-102 Ba-145 I-138 Y-98 Te-136 Se-86 Zr-99 Sb-132 Q (MeV) P-Index 7.31 5.89 6.22 5.88 8.25 6.69 0.47 4.40 7.57 0.67 6.01 0.30 9.23 0.54 6.85 5.53 0.89 8.96 7.50 7.63 4.14 4.22 6.86 10.29 0.41 7.66 5.58 4.11 4.77 0.80 5.57 7.82 0.32 8.82 0.50 5.09 0.36 5.14 0.48 4.34 5.51 Half-life 1.68 s 19.0 s 1.06 m 24.5 s 5.34 s 3.75 s 32.3 s? 1.48 s 1.84 s 2.0 s 55.6 s 1.5 s 16.5 s 46.9 s 55.0 s 7.42 m 24.2 m 1.39 m 2.70 s 426 ms 18.3 m 24.8 s 2.9 s 4.31s 6.41 s 548 ms 17.6 s 15.3 s 2.1 s 2.79 m Contribution 4.51E-04 4.48E-04 4.39E-04 4.11E-04 4.06E-04 3.95E-04 3.93E-04 3.83E-04 3.67E-04 3.54E-04 3.48E-04 3.45E-04 3.35E-04 3.16E-04 3.03E-04 3.02E-04 2.95E-04 2.92E-04 2.89E-04 2.86E-04 2.75E-04 2.71E-04 2.66E-04 2.56E-04 2.53E-04 2.30E-04 2.23E-04 2.15E-04 2.12E-04 2.10E-04 Green: Idaho TAGS Blue: Jyvaskyla TAGS Orange: Jyvaskyla undergoing in 2009 Brown: On Request List in INDC(NDA)-0551 Table FPs Contributing to Neutrino Spectrum from Pu-239 at 4MeV (These Top 30 Nuclides Cover 60% of the Total ) ZA 43104 43102 41098 41101 39094 55138 41100 42105 53134 57142 41102 39095 41103 38095 55141 40099 39097 55139 54137 39096 54139 40101 43106 37091 37092 39098 43107 57144 38096 53136 Nuclide Tc-104 Tc-102 Nb-98 Nb-101 Y-94 Cs-138 Nb-100 Mo-105 I-134 La-142 Nb-102 Y-95 Nb-103 Sr-95 Cs-141 Zr-99 Y-97m Cs-139 Xe-137 Y-96 Xe-139 Zr-101 Tc-106 Rb-91 Rb-92 Y-98m Tc-107 La-144 Sr-96 I-136m Q (MeV) 5.58 4.53 4.58 4.57 4.92 5.38 6.25 4.95 4.05 4.50 7.21 4.45 5.53 6.09 5.25 4.70 7.36 4.21 4.16 8.25 5.06 5.77 6.55 5.91 8.09 9.23 4.82 5.54 5.41 7.50 P-Index 0.16 0.61 0.54 0.63 Half-life 18.3 m 54.2 s 2.86 s 7.1 s 18.7 m 33.4 m 1.5 s 35.6 s 3.52 m 1.52 h 4.3 s 10.3 s 1.5 s 23.9 s 24.8 s 2.1 s 1.17 s 9.27 m 3.82 m 5.34 s 39.7 s 2.3 s 35.6 s 58.4 s 4.49 s 2.0 s 21.2 s 40.8 s 1.07 s 46.9 s Contribution 8.91E-04 8.85E-04 8.66E-04 7.76E-04 7.25E-04 6.64E-04 6.63E-04 6.23E-04 6.16E-04 5.74E-04 5.63E-04 5.59E-04 5.28E-04 5.18E-04 4.92E-04 4.68E-04 4.54E-04 4.54E-04 4.51E-04 4.51E-04 4.18E-04 4.12E-04 4.10E-04 3.99E-04 3.81E-04 3.80E-04 3.69E-04 3.60E-04 3.58E-04 3.54E-04 Blue: Jyvaskyla TAGS Green: Idaho TAGS Red: Jyvaskyla IEEE(2013) Brown: On Request List in INDC(NDA)-0551 Table FPs Contributing to Neutrino Spectrum from U-235 at 8MeV (These Top 30 Nuclides Cover 95% of the Total ) ZA 37092 35088 39098 37094 37095 39096 39098 33086 39100 35090 35089 37096 35091 36093 33088 33084 51134 39101 41104 32086 40105 55144 39102 33085 33087 37100 51134 41104 34089 48130 Nuclide Q (MeV) Hal-life Contribution Rb-92 8.09 4.49 s 2.49E-05 Br-88 8.96 16.5 s 2.33E-05 Y-98m 9.23 2.0 s 2.30E-05 Rb-94 10.29 2.70 s 2.10E-05 Rb-95 9.28 378 ms 1.46E-05 Y-96 8.25 5.34 s 1.33E-05 Y-98 8.82 548 ms 1.26E-05 As-86 11.54 0.95 s 1.18E-05 Y-100m 9.46 940 ms 1.07E-05 Br-90 10.35 1.92 s 6.61E-06 Br-89 8.16 4.40 s 5.74E-06 Rb-96 11.75 201 ms 5.38E-06 Br-91 9.80 541 ms 4.80E-06 Kr-93 8.49 1.29 s 4.69E-06 As-88 12.60 92.1 ms 4.15E-06 As-84 10.09 4.5 s 4.01E-06 Sb-134m 8.80 10.0 s 3.17E-06 Y-101 8.55 0.45 s 3.00E-06 Nb-104m 8.33 0.94 s 2.80E-06 Ge-86 8.00 88 ms 2.13E-06 Zr-105 9.39 600 ms 2.03E-06 Cs-144 8.50 0.99 s 1.94E-06 Y-102 9.85 300 ms 1.86E-06 As-85 9.23 2.03 s 1.49E-06 As-87 10.81 0.48 s 1.49E-06 Rb-100 13.10 51 ms 1.42E-06 Sb-134 8.39 0.78 s 1.08E-06 Nb-104 8.11 4.8 s 1.03E-06 Se-89 9.39 0.41 s 9.45E-07 Cd-130 8.35 162 ms 8.92E-07 Orange: Jyvaskyla undergoing in 2009 Red: Jyvaskyla IEEE(2013) Brown: On Request List in INDC(NDA)-0551 Number of Electrons per MeV 1.00E+00 1.00E-01 1.00E-02 Gross Theory (GT2) JENDL (2011) 1.00E-03 1.00E-04 0 1 2 3 4 5 6 7 Energy (MeV) Fig. Electron Energy Spectrum from Rb-92 Beta-Decay 8 9 3.00E-01 Gross Theory (GT2) JENDL (2011) Number of Electrons per MeV 2.50E-01 2.00E-01 1.50E-01 1.00E-01 5.00E-02 0.00E+00 0 1 2 3 4 5 6 7 Energy (MeV) Fig. Electron Energy Spectrum from Rb-92 Beta-Decay 8 9 S.Chiba, T.Yoshida, T.Tachibana, N.Hagura, Proc. AESJ Fall Mtg., (2014) L55, Kyoto Electron Energy (MeV) Fig. Comparison between Measured and Calculated U-235 Electron Spectra (Calculated with Summation Method fully based on the Gross Theory) Fractional Contribution (cumulative) 1.0 0.9 12 MeV 10 MeV 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 Number of Contributing FPs Fig. Number of Contributors to U-235 Neutrino Spectra at 10 & 12MeV Table List of FPs Contributiong to U-235 Beta-Particle Number Spectrum at High Energy At 8 MeV Fractional Contribution (cumulative) Rb-94 10.29 0.15 Y-98m 9.23 0.28 Br-88 8.96 0.39 Rb-95 9.28 0.46 As-86 11.54 0.53 Y-100m 9.46 0.59 Y-98 8.82 0.64 Br-90 10.35 0.69 Rb-96 11.75 0.72 Br-91 9.80 0.75 As-84 10.09 0.78 As-88 12.60 0.81 Y-96 8.25 0.82 Rb-092 8.09 0.84 Y-102 9.85 0.85 Kr-93 8.49 0.86 Sb-134m 8.80 0.87 As-87 10.81 0.88 Zr-105 9.39 0.90 Rb-100 13.10 0.91 Y-101 8.55 0.91 As-85 9.23 0.92 Rb-097 10.38 0.93 Nb-104m 8.33 0.93 Se-89 9.39 0.94 Cd-131 12.40 0.94 Br-89 8.16 0.95 Cs-144 8.50 0.95 Br-92 12.20 0.96 Y-100 9.31 0.96 Odd-Odd Fraction: 57% Nuclide Q-Value (MeV) At 10 MeV Nuclide Q-Value (MeV) As-86 Rb-96 Rb-94 As-88 Br-90 Rb-100 As-87 Cd-131 Br-92 In-131n In-132 Ga-82 Ga-84 As-84 Rb-97 In-130 Ge-87 Rb-98m Ga-80 Rb-98 Y-97m Br-93 In-130n Se-091 Y-104 Ge-85 Ag-124 11.54 11.75 10.29 12.60 10.35 13.10 10.81 12.40 12.20 12.74 14.14 12.48 13.70 10.09 10.38 10.25 11.40 12.69 10.31 12.42 10.22 11.10 10.65 10.80 10.80 10.07 10.23 70% Fractional Contribution (cumulative) 0.39 0.53 0.66 0.78 0.83 0.87 0.90 0.92 0.94 0.95 0.96 0.97 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 At 12 MeV Q-Value (MeV) Nuclide As-88 Rb-100 Ga-84 In-132 In-131n Cd-131 Ga-82 Br-92 Rb-98m Rb-98 12.60 13.10 13.70 14.14 12.74 12.40 12.48 12.20 12.69 12.42 80% Fractional Contribution (cumulative) 0.47 0.75 0.81 0.87 0.92 0.95 0.97 0.99 1.00 1.00 Courtesy T.Tachibana, Waseda Univ. Modelling of Odd-Odd Nucleus In the Gross Theory of Beta-Decay eF d12 d11 D1 e1 Neutron 𝑑𝑛1 𝑑ԑ DW(E,e) Proton D2 d2 d2 A ≤ 70 eF d12 d11 D1 e1 DW(E,e) Basis ee 𝑑𝑛1 𝑑ԑ D2 d2 d2 A ≤ 70 oo Courtesy T.Tachibana, Waseda Univ. d13 D1 eF d12 d11 e1 D1 𝑑𝑛1 𝑑ԑ DW(E,e) D2 Basis ee oo d2 d2 A ≤ 70 d13 D1 eF d12 d11 e1 D1 𝑑𝑛1 𝑑ԑ DW(E,e) D2 Basis ee oo d2 d2 d2 D2 d2 A ≤ 70 d13 D1 eF d12 d11 e1 D1 𝑑𝑛1 𝑑ԑ E2nd Emax DW(E,e) D2 Basis ee oo d2 d2 d2 D2 d2 A ≤ 70 Table List of FPs Contributiong to U-235 Beta-Particle Number Spectrum at High Energy Revisited At 8 MeV Fractional Contribution (cumulative) Rb-94 10.29 0.15 Y-98m 9.23 0.28 Br-88 8.96 0.39 Rb-95 9.28 0.46 As-86 11.54 0.53 Y-100m 9.46 0.59 Y-98 8.82 0.64 Br-90 10.35 0.69 Rb-96 11.75 0.72 Br-91 9.80 0.75 As-84 10.09 0.78 As-88 12.60 0.81 Y-96 8.25 0.82 Rb-092 8.09 0.84 Y-102 9.85 0.85 Kr-93 8.49 0.86 Sb-134m 8.80 0.87 As-87 10.81 0.88 Zr-105 9.39 0.90 Rb-100 13.10 0.91 Y-101 8.55 0.91 As-85 9.23 0.92 Rb-097 10.38 0.93 Nb-104m 8.33 0.93 Se-89 9.39 0.94 Cd-131 12.40 0.94 Br-89 8.16 0.95 Cs-144 8.50 0.95 Br-92 12.20 0.96 Y-100 9.31 0.96 Odd-Odd Fraction: 57% Nuclide Q-Value (MeV) At 10 MeV Nuclide Q-Value (MeV) As-86 Rb-96 Rb-94 As-88 Br-90 Rb-100 As-87 Cd-131 Br-92 In-131n In-132 Ga-82 Ga-84 As-84 Rb-97 In-130 Ge-87 Rb-98m Ga-80 Rb-98 Y-97m Br-93 In-130n Se-091 Y-104 Ge-85 Ag-124 11.54 11.75 10.29 12.60 10.35 13.10 10.81 12.40 12.20 12.74 14.14 12.48 13.70 10.09 10.38 10.25 11.40 12.69 10.31 12.42 10.22 11.10 10.65 10.80 10.80 10.07 10.23 70% Fractional Contribution (cumulative) 0.39 0.53 0.66 0.78 0.83 0.87 0.90 0.92 0.94 0.95 0.96 0.97 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 At 12 MeV Q-Value (MeV) Nuclide As-88 Rb-100 Ga-84 In-132 In-131n Cd-131 Ga-82 Br-92 Rb-98m Rb-98 12.60 13.10 13.70 14.14 12.74 12.40 12.48 12.20 12.69 12.42 80% Fractional Contribution (cumulative) 0.47 0.75 0.81 0.87 0.92 0.95 0.97 0.99 1.00 1.00 Br Rb As Atomic Number Z ( A= 88 Fixed ) Fig. Comparison of Charge Yield between Major Nuclear Data Libraries for U-235 Thermal Neutron Fission As Ga Atomic Number Z ( A= 84 Fixed ) Fig. Comparison of Charge Yield between Major Nuclear Data Libraries for U-235 Thermal Neutron Fission Thank you for Your Attention