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