18.08.2015   NUCLEAR CHEMICAL ENGINEERING

Neutron Absorption by Long-lived Fission Products

Also shown in Table 8.2 are the effective thermal cross sections for the individual nuclides, calculated for the neutron spectrum of a typical PWR and including the contributions from resonance absorption. The cross sections are multiplied by the atoms per fission-product pair to obtain the effective cross sections per fission-product pair listed in Table 8.2. Although the total effective cross section of 89.2 b/fission-product pair is calculated for the mixture of radionuclides existing 150 days after fuel discharge, it is a good approximation for the effective

^Acts both as an acid and as a base.

Half-life

Atoms per

fission-

product

Effective

thermal

cross

Neutron absorption, bams per fission-product

Nuclide

(S = stable)

pair*

sections, § b

pair

3H

12.3 yr

1.26 X 10~4

—

—

73 Ge

S

1.38 X 10’6

11.5

1.59 X 10’5

74 Ge

S

4.94 X 10’6

0.369

1.83 X 10’6

76 Ge

s

2.61 X 10’s

0.295

7.70 X 10‘6

Total11

3.29 X 10‘s

2.54 X 10’s

73 As

s

7.98 X 10‘6

14.5

1.16 X 10’4

Total

7.98 X 10~6

1.16 X 10~4

77 Se

s

8.06 X 10’s

42.7

3.44 X 10-3

78 Se

s

2.16 X 10*4

0.352

7.60 X 10’s

79 Se

<6.5 X 104 yr

5.00 X 10~4

3.74

1.87 X 10’3

80 Se

s

9.05 X 10’4

0.737

6.67 X 10’4

82 Se

S

2.87 X 10~3

1.638

4.70 X 10’3

Total

4.58 X 10~3

1.08 X 10-2

81 Br

S

1.29 X 10’3

20.0

2.58 X 10’2

Total

1.29 X 10’3

2.58 X 10’2

82 Kr

S

2.75 X 10’5

93.0

2.56 X 10’3

83 Kr

S

3.51 X 10’3

222

7.79 X 10’1

84 Kr

s

9.73 X 10’3

1.47

1.43 X 10’2

85 Kr

10.76 yr

2.48 X 10’3

9.89

2.45 X 10’2

86 Kr

S

1.65 X 10’2

0.065

1.07 X 10’3

Total

3.22 X 10‘2

8.22 X 10’1

85 Rb

s

8.14 X 10‘3

0.937

7.63 X 10’3

87 Rb

4.7 X 1010 yr

2.03 X 10’2

0.147

2.98 X 10’3

Total

2.84 X 10’2

1.06 X 10-2

88 Sr

S

2.94 X 10~2

0.005

1.47 X 10’4

89 Sr

52 days

2.82 X 10‘4

0.466

1.31 X 10‘4

90 Sr

28.1 yr

4.43 X 10~2

1.34

5.94 X 10‘2

Total

7.40 X 10*2

5.96 X 10~2

89 у

S

3.82 X 10’2

1.29

4.93 X 10’2

«Y

64 h

1.16 X 10’4

3.27

3.79 X 10‘4

91Y

58.8 days

1.06 X 10’3

0.996

1.06 X 10*3

Total

3.87 X 10’2

5.07 X 10’2

90 Zr

S

2.05 X 10*3

0.093

1.91 X 10’4

91 Zr

S

4.81 X 10~2

3.81

1.83 X 10_1

92 Zr

S

5.19 X 10‘2

0.363

1.88 X 10’2

93 Zr

1.5 X 106 yr

5.65 X 10~2

8.93

5.05 X 10_1

94 Zr

S

5.92 X 10’2

0.118

6.99 X 10~3

95 Zr

65 days

9.20 X 10’4

~ 0

—

96 Zr

>3.6 X 1017 yr

6.00 X 10~2

0.063

3.78 X 10‘3

Total

2.78 X 10’1

7.18 X 10"1

95 Nb

35.0 days

9.28 X 10’4

4.10

3.80 X 10-3

Total

9.35 X 10’4

3.80 X 10’3

Half-life

Atoms per

fission-

product

Effective

thermal

cross

Neutron absorption, barns per fission-product

Nuclide

(S = stable)

pair*

sections,** b

pair

О

s

■A

S

5,47 X НГ2

40.8

2.23

96 Mo

s

2,50 X 10‘3

8.44

2.11 X 10’2

97 Mo

s

5.93 X 10‘2

6.39

3.79 X 10_1

98 Mo

s

5.88 X 10*2

2.04

1.20 X 10_1

100 Mo

>3 X 1017 yr

6.52 X 10‘2

1.60

1.04 X 10’1

Total

2.40 X 10’1

2.86

99 Tc

2.12 X 10s yr

5.77 X 10~2

44.4

2.56

Total

5.77 X 10’2

2.56

100 Ru

S

2.89 X 10‘3

10.9

3.15 X 10’2

101 Ru

S

5.19 X 10’2

25.1

1.30

102 Ru

S

4.90 X 10’2

4.33

2.12 X 10’1

103 Ru

39.6 days

1.66 X 10"4

~ 0

—

104 Ru

S

3.10 X 10~2

1.70

5.20 X 10’2

106 Ru

367 days

6.28 X 10‘3

0.693

4.35 X 10’3

Total

1.41 X 10"1

1.60

103 Rh

S

2.36 X 10~2

426

1.01 X 101

Total

2.36 X 10~2

1.01 X 101

104 Pd

S

9.43 X 10’3

10.4

9.81 X 10’2

105 Pd

S

1.67 X 10’2

30.8

5.14 X 10’1

106 pd

S

1,42 X 10‘2

1.95

2.77 X 10’2

107 Pd

7 X 106 yr

1.16 X 10’2

19.6

2.27 X 10’1

108 Pd

S

7.35 X 10’3

54.2

3.98 X 10’1

no pd

s

1.56 X 10"3

3.06

4.77 X 10‘3

Total

6.71 X 10‘2

1.27

109 Ag

s

2.94 X 10~3

487

1.43

Total

2.94 X 10‘3

1.43

noCd

s

1.14 X 10~3

8.76

9.99 X 10’3

111 Cd

s

8.06 X 10‘4

16.54

1.33 X 10’2

112 Cd

s

4.30 X 10"4

3.75

1.61 X 10’3

113 Cd

s

9.35 X 10’6

1.66 X 104

1.55 X 10_1

114 Cd

s

6.50 X 10’4

6.78

4.41 X 10’3

116 Cd

s

1.95 X 10‘4

2.06

4.02 X 10‘4

Total

3.23 X 10’3

1.85 X 10_1

115 In

6 X 1014 yr

7.24 X 10"5

1.14 X 103

8.25 X 10’2

Total

7.24 X 10’5

8.25 X 10’2

116 Sn

s

1.06 X 10’4

4.02

4.26 X 10‘4

117 Sn

s

2.02 X 10’4

6.80

1.37 X 10"3

118 Sn

s

2.05 X 10’4

~ 0

—

I19Sn

s

2.11 X 10‘4

3.94

8.31 X 10’4

120 Sn

s

2.21 X 10’4

0.347

7.67 X 10‘s

122 Sn

s

2.56 X 10’4

0.147

3.76 X 10‘s

124 Sn

s

3.69 X 10-4

0.115

4.24 X 10*5

Half-life

Atoms per

fission-

product

Effective

thermal

cross

Neutron absorption, barns per fission-product

Nuclide

(S = stable)

pair*

sections,^ b

pair

124 Sn

®10s yr

4.71 X 10"4

0.280

1.32 X 10~4

Total

2.05 X 10’3

2.92 X 10’3

121 Sb

S

2.32 X 10’4

46.3

1.07 X 10’2

123 Sb

> 1.3 X 1014 yr

2.72 X 10‘4

54.6

1.49 X 10"2

125 Sb

2.71 yr

3.36 X 10~4

1.46

4.91 X 10’4

Total

8.44 X 10’4

2.61 X 10’2

125mTe

58 days

7.98 X 10’4

—

_

125 Те

S

1.59 X 10’4

8.16

1.30 X 10’3

126 Те

S

4.50 X 10’4

3.32

1.49 X 10~3

ШШТе

109 days

2.98 X 10"s

—

—

128 Те

S

6.21 X 10’3

3.00

1.86 X 10’2

129mTe

34 days

1.03 X 10_s

_

—

із° те

8 X 1020 yr

2.16 X 10’2

0.270

5.83 X 10-3

Total

2.85 X 10‘2

2.73 X 10’2

1271

S

1.79 X 10’3

55.8

9.99 X 10’2

129 j

1.7 X 107 yr

1.07 X 10’2

37.4

4.00 X 10’1

Total

1.25 X 10‘2

5.00 X 10’1

130 Xe

S

3.95 X 10‘4

2.46

9.72 X 10’4

131 Xe

s

2.18 X 10‘2

322

7.02

132 Xe

s

5.68 X 10‘2

0.869

4.94 X 10’2

134 Xe

s

7.83 X 10’2

0.689

5.39 X 10*2

134 Xe

s

1.19 X 10*1

0.230

2.74 X 10‘2

Total

2.76 X 10"]

7.15

133 Cs

s

5.37 X 10’2

158

8.48

134 Cs

2.046 yr

6.94 X 10’3

129

8.95 X 10’1

135 Cs

3.0 X 104 yr

1.42 X 10’2

30.2

4.29 X 10’1

137 Cs

30.0 yr

6.02 X 10’2

0.176

1.06 X 10’2

Total

1.35 X 10’1

9.82

134 Ba

S

3.91 X 10-3

0.819

3.20 X 10’3

134 Ba

S

9.20 X 10’4

4.05

3.73 X 10-3

137 Ba

S

2.37 X 10’3

4.75

1.13 X 10-2

138 Ba

S

5.91 X 10’2

0.574

3.39 X 10’2

Total

6.63 X 10’2

5.21 X 10‘2

139 La

S

6.25 X 10‘2

9.87

6.17 X 10’1

Total

6.25 X 10‘2

6.17 X 10’1

140 Ce

S

6.37 X 10’2

0.631

4.02 X 10‘2

141 Ce

33 days

9.66 X 10’5

23.7

2.29 X 10-3

142 Ce

>5 X 1014 yr

5.73 X 10’2

1.15

6.59 X 10~2

144 Ce

284 days

1.16 X 10’2

1.57

1.82 X 10‘2

Total

1.33 X 10’1

1.27 X 10"1

Nuclide

Half-life (S = stable)

Atoms per fission — product pair*

Effective

thermal

cross

sections, § b

Neutron absorption, bams per fission-product pair

141 Pr

>2X 1016 yr

5.90 X 10’2

6.40

3.78 X 10’1

Total

5.90 X 10’2

3.78 X 10‘1

142 Nd

S

8.75 X 10’4

16.8

1.47 X 10‘2

143 Nd

S

3.69 X 10’2

288

1.06 X 101

144 Nd

2.4 X 1013 yr

5.23 X 10~2

7.54

3.94 X 10’1

143 Nd

>6X 1016 yr

3.43 X 10‘2

86.7

2.97

146 Nd

S

3.37 X 10‘2

15.4

5.19 X 10’1

148 Nd

S

1.75 X 10~2

7.74

1.35 X 10’1

130 Nd

>1016 yr

8.37 X 10‘3

6.47

5.42 X 10’2

Total

1.84 X 10’1

1.47 X 101

147 Pm

2.62 yr

5.70 X 10’3

1.11 X 103

6.33

Total

5.70 X 10’3

6.33

147 Sm

1.05 X 10u yr

3.67 X 10"3

274

1.01

148 Sm

> 2 X 1014 yr

1.04 X 10~2

21.7

2.26 X 10’1

149 Sm

> 1 X 1013 yr

2.19 X 10‘4

3.52 X 104

7.71

130 Sm

S

1.35 X 10’2

149

2.01

151 Sm

«87 yr

1.70 X 10’3

2.17 X 103

3.88

132 Sm

S

4.46 X 10’3

1.03 X 103

4.59

134 Sm

S

1.43 X 10‘3

11.7

1.67 X 10’2

Total

3.54 X 10’2

1.94 X 101

133 Eu

s

4.70 X 10’3

629

2.96

134 Eu

16 yr

1.39 X 10‘3

1.32 X 103

1.83

133 Eu

1.811 yr

1.56 X 10~4

1.22 X 104

1.90

Total

6.26 X 10"3

6.69

133 Gd

S

2.84 X 10’3

4.51 X 104

1.28

138 Gd

S

2.49 X 10~3

16.0

3.98 X 10’2

137 Gd

S

1.20 X 10’6

2.08 X 103

2.50 X 10’1

138 Gd

S

4.33 X 10"4

11.18

4.84 X 10’3

160 Gd

S

3.06 X 10*3

0.655

2.00 X 10*3

Total

3.06 X 10’3

1.58

139 Tb

S

5.90 X 10’3

218

1.28 X 10’2

Total

5.90 X 10‘3

1.28 X 10*2

160 Dy

s

1.06 X 10~3

377

4.00 X 10’3

161 Dy

s

6.96 X 10‘6

970

6.75 X 10’3

162 Dy

s

6.01 X 10‘6

1.08 X 103

6.50 X 10’3

163 Dy

s

4.92 X 10‘6

664

3.27 X 10’3

164 Dy

s

1.16 X 10’6

2.32 X 103

2.69 X 10*3

Total

2.96 X 10’3

2.32 X lO’2

Total, all fission products

2.00

89.2

^One hundred fifty days after discharge from uranium-fueled PWR.

* Some elemental totals include minor contributions for nuclides not shown in table.

8 Effective thermal cross sections for a typical neutron spectrum of a PWR, including contribu­tions from nonthermal resonance absorption.

1 Total yield of element whose principal radionuclides are listed above

Figure 8.2 Chemical composition of fission products (for uranium-fueled PWR 150 days after discharge).

cross section for all fission products other than 135Xe at the time of fuel discharge. Except for 135Xe, the shorter-lived species that are also present at the time of discharge do not exist in sufficient concentration to contribute appreciably to neutron absorption. Neutron absorption in 13SXe is usually treated separately, by the techniques discussed in Sec. 6.3 of Chap. 2.

The elemental contribution to neutron absorption by fission products tends to follow the effective fission yield of the elements, but with exceptions for several individual elements. The rare earths neodymium, promethium, samarium, europium, and gadolinium, as well as xenon and cesium, are the important neutron-absorbing elements resulting from the high-mass fission-yield peak, and rhodium and its near neighbors are the important neutron absorbers from the low-mass peak.