Nuclear fission splits a heavy nucleus such as uranium or plutonium into two lighter nuclei, which are called fission products. Yield refers to the fraction of a fission product produced per fission.
Isotope and element yields will change as the fission products undergo beta decay, while chain yields do not change after completion of neutron emission by a few neutron-rich initial fission products (delayed neutrons), with half-life measured in seconds.
A few isotopes can be produced directly by fission, but not by beta decay because the would-be precursor with atomic number one less is stable and does not decay (atomic number grows by 1 during beta decay). Chain yields do not account for these "shadowed" isotopes; however, they have very low yields (less than a millionth as much as common fission products) because they are far less neutron-rich than the original heavy nuclei.
Yield is usually stated as percentage per fission, so that the total yield percentages sum to 200%. Less often, it is stated as percentage of all fission products, so that the percentages sum to 100%. Ternary fission, about 0.2–0.4% of fissions, also produces a third light nucleus such as helium-4 (90%) or tritium (7%).
Mass vs. yield curve
If a graph of the mass or mole yield of fission products against the atomic number of the fragments is drawn then it has two peaks, one in the area zirconium through to palladium and one at xenon through to neodymium. This is because the fission event causes the nucleus to split in an asymmetric manner,[1] as nuclei closer to magic numbers are more stable.[2]
Yield vs. Z - This is a typical distribution for the fission of uranium. Note that in the calculations used to make this graph the activation of fission products was ignored and the fission was assumed to occur in a single moment rather than a length of time. In this bar chart results are shown for different cooling times (time after fission).
Because of the stability of nuclei with even numbers of protons and/or neutrons the curve of yield against element is not a smooth curve. It tends to alternate.
In general, the higher the energy of the state that undergoes nuclear fission, the more likely a symmetric fission is, hence as the neutron energy increases and/or the energy of the fissile atom increases, the valley between the two peaks becomes more shallow; for instance, the curve of yield against mass for Pu-239 has a more shallow valley than that observed for U-235, when the neutrons are thermal neutrons. The curves for the fission of the later actinides tend to make even more shallow valleys. In extreme cases such as 259Fm, only one peak is seen.
Yield is usually expressed relative to number of fissioning nuclei, not the number of fission product nuclei, that is, yields should sum to 200%.
The yields in the table sum to only 45.5522%, including 34.8401% which have half-lives greater than one year:
t½ in years
Yield
1 to 5
2.7252%
10 to 100
12.5340%
2 to 300,000
6.1251%
1.5 to 16 million
13.4494%
The remainder and the unlisted 54.4478% decay with half-lives less than one year into nonradioactive nuclei.
This is before accounting for the effects of any subsequent neutron capture; e.g.:
135Xe capturing a neutron and becoming nearly stable 136Xe, rather than decaying to 135Cs which is radioactive with a half-life of 2.3 million years
Nonradioactive 133Cs capturing a neutron and becoming 134Cs, which is radioactive with a half-life of 2 years
Many of the fission products with mass 147 or greater such as 147Pm, 149Sm, 151Sm, and 155Eu have significant cross sections for neutron capture, so that one heavy fission product atom can undergo multiple successive neutron captures.
Besides fission products, the other types of radioactive products are
Neutron capture (29 barns) slowly converts stable 133Cs to 134Cs, which itself is low-yield because beta decay stops at 134Xe; can be further converted (140 barns) to 135Cs.
Source of much of the decay heat together with 137 Cs on the timespan of years to decades after irradiation. Formerly used in radioisotope thermoelectric generators.
Neutron poison, most will be destroyed while fuel still in use.
Cumulative fission yields
Cumulative fission yields give the amounts of nuclides produced either directly in the fission or by decay of other nuclides.
Cumulative fission yields per fission for U-235 (%)[4]
Product
Thermal fission yield
Fast fission yield
14-MeV fission yield
1 1H
0.00171 ± 0.00018
0.00269 ± 0.00044
0.00264 ± 0.00045
2 1H
0.00084 ± 0.00015
0.00082 ± 0.00012
0.00081 ± 0.00012
3 1H
0.0108 ± 0.0004
0.0108 ± 0.0004
0.0174 ± 0.0036
3 2He
0.0108 ± 0.0004
0.0108 ± 0.0004
0.0174 ± 0.0036
4 2He
0.1702 ± 0.0049
0.17 ± 0.0049
0.1667 ± 0.0088
85 35Br
1.304 ± 0.012
1.309 ± 0.043
1.64 ± 0.31
82 36Kr
0.000285 ± 0.000076
0.00044 ± 0.00016
0.038 ± 0.012
85 36Kr
0.286 ± 0.021
0.286 ± 0.026
0.47 ± 0.1
85m 36Kr
1.303 ± 0.012
1.307 ± 0.043
1.65 ± 0.31
90 38Sr
5.73 ± 0.13
5.22 ± 0.18
4.41 ± 0.18
95 40Zr
6.502 ± 0.072
6.349 ± 0.083
5.07 ± 0.19
94 41Nb
0.00000042 ± 0.00000011
2.90±0.770 × 10−8
0.00004 ± 0.000015
95 41Nb
6.498 ± 0.072
6.345 ± 0.083
5.07 ± 0.19
95m 41Nb
0.0702 ± 0.0067
0.0686 ± 0.0071
0.0548 ± 0.0072
92 42Mo
0 ± 0
0 ± 0
0 ± 0
94 42Mo
8.70 × 10−10 ± 3.20 × 10−10
0 ± 0
6.20 × 10−8 ± 2.50 × 10−8
96 42Mo
0.00042 ± 0.00015
0.000069 ± 0.000025
0.0033 ± 0.0015
99 42Mo
6.132 ± 0.092
5.8 ± 0.13
5.02 ± 0.13
99 43Tc
6.132 ± 0.092
5.8 ± 0.13
5.02 ± 0.13
103 44Ru
3.103 ± 0.084
3.248 ± 0.042
3.14 ± 0.11
106 44Ru
0.41 ± 0.011
0.469 ± 0.036
2.15 ± 0.59
106 45Rh
0.41 ± 0.011
0.469 ± 0.036
2.15 ± 0.59
121m 50Sn
0.00106 ± 0.00011
0.0039 ± 0.00091
0.142 ± 0.023
122 51Sb
0.000000366 ± 0.000000098
0.0000004 ± 0.00000014
0.00193 ± 0.00068
124 51Sb
0.000089 ± 0.000021
0.000112 ± 0.000034
0.027 ± 0.01
125 51Sb
0.026 ± 0.0014
0.067 ± 0.011
1.42 ± 0.42
132 52Te
4.276 ± 0.043
4.639 ± 0.065
3.85 ± 0.16
129 53I
0.706 ± 0.032
1.03 ± 0.26
1.59 ± 0.18
131 53I
2.878 ± 0.032
3.365 ± 0.054
4.11 ± 0.14
133 53I
6.59 ± 0.11
6.61 ± 0.13
5.42 ± 0.4
135 53I
6.39 ± 0.22
6.01 ± 0.18
4.8 ± 1.4
128 54Xe
0 ± 0
0 ± 0
0.00108 ± 0.00048
130 54Xe
0.000038 ± 0.0000098
0.000152 ± 0.000055
0.038 ± 0.014
131m 54Xe
0.0313 ± 0.003
0.0365 ± 0.0031
0.047 ± 0.0049
133 54Xe
6.6 ± 0.11
6.61 ± 0.13
5.57 ± 0.41
133m 54Xe
0.189 ± 0.015
0.19 ± 0.015
0.281 ± 0.049
135 54Xe
6.61 ± 0.22
6.32 ± 0.18
6.4 ± 1.8
135m 54Xe
1.22 ± 0.12
1.23 ± 0.13
2.17 ± 0.66
134 55Cs
0.0000121 ± 0.0000032
0.0000279 ± 0.0000073
0.0132 ± 0.0035
137 55Cs
6.221 ± 0.069
5.889 ± 0.096
5.6 ± 1.3
140 56Ba
6.314 ± 0.095
5.959 ± 0.048
4.474 ± 0.081
140 57La
6.315 ± 0.095
5.96 ± 0.048
4.508 ± 0.081
141 58Ce
5.86 ± 0.15
5.795 ± 0.081
4.44 ± 0.2
144 58Ce
5.474 ± 0.055
5.094 ± 0.076
3.154 ± 0.038
144 59Pr
5.474 ± 0.055
5.094 ± 0.076
3.155 ± 0.038
142 60Nd
6.30 × 10−9 ± 1.70 × 10−9
1.70 × 10−9 ± 4.80 × 10−10
0.0000137 ± 0.0000049
144 60Nd
5.475 ± 0.055
5.094 ± 0.076
3.155 ± 0.038
147 60Nd
2.232 ± 0.04
2.148 ± 0.028
1.657 ± 0.045
147 61Pm
2.232 ± 0.04
2.148 ± 0.028
1.657 ± 0.045
148 61Pm
5.00 × 10−8 ± 1.70 × 10−8
7.40 × 10−9 ± 2.50 × 10−9
0.0000013 ± 0.00000042
148m 61Pm
0.000000104 ± 0.000000039
1.78 × 10−8 ± 6.60 × 10−9
0.0000048 ± 0.0000018
149 61Pm
1.053 ± 0.021
1.064 ± 0.03
0.557 ± 0.09
151 61Pm
0.4204 ± 0.0071
0.431 ± 0.015
0.388 ± 0.061
148 62Sm
0.000000149 ± 0.000000041
2.43 × 10−8 ± 6.80 × 10−9
0.0000058 ± 0.0000018
150 62Sm
0.000061 ± 0.000022
0.0000201 ± 0.0000077
0.00045 ± 0.00018
151 62Sm
0.4204 ± 0.0071
0.431 ± 0.015
0.388 ± 0.061
153 62Sm
0.1477 ± 0.0071
0.1512 ± 0.0097
0.23 ± 0.015
151 63Eu
0.4204 ± 0.0071
0.431 ± 0.015
0.388 ± 0.061
152 63Eu
3.24 × 10−10 ± 8.50 × 10−11
0 ± 0
3.30 × 10−8 ± 1.10 × 10−8
154 63Eu
0.000000195 ± 0.000000064
4.00 × 10−8 ± 1.10 × 10−8
0.0000033 ± 0.0000011
155 63Eu
0.0308 ± 0.0013
0.044 ± 0.01
0.088 ± 0.014
Cumulative fission yield per fission for Pu-239 (%)[4]
Product
Thermal fission yield
Fast fission yield
14-MeV fission yield
1 1H
0.00408 ± 0.00041
0.00346 ± 0.00057
-
2 1H
0.00135 ± 0.00019
0.00106 ± 0.00016
-
3 1H
0.0142 ± 0.0007
0.0142 ± 0.0007
-
3 2He
0.0142 ± 0.0007
0.0142 ± 0.0007
-
4 2He
0.2192 ± 0.009
0.219 ± 0.009
-
85 35Br
0.574 ± 0.026
0.617 ± 0.049
-
82 36Kr
0.00175 ± 0.0006
0.00055 ± 0.0002
-
85 36Kr
0.136 ± 0.014
0.138 ± 0.017
-
85m 36Kr
0.576 ± 0.026
0.617 ± 0.049
-
90 38Sr
2.013 ± 0.054
2.031 ± 0.057
-
95 40Zr
4.949 ± 0.099
4.682 ± 0.098
-
94 41Nb
0.0000168 ± 0.0000045
0.00000255 ± 0.00000069
-
95 41Nb
4.946 ± 0.099
4.68 ± 0.098
-
95m 41Nb
0.0535 ± 0.0066
0.0506 ± 0.0062
-
92 42Mo
0 ± 0
0 ± 0
-
94 42Mo
3.60 × 10−8 ± 1.30 × 10−8
4.80 × 10−9 ± 1.70 × 10−9
-
96 42Mo
0.0051 ± 0.0018
0.0017 ± 0.00062
-
99 42Mo
6.185 ± 0.056
5.82 ± 0.13
-
99 43Tc
6.184 ± 0.056
5.82 ± 0.13
-
103 44Ru
6.948 ± 0.083
6.59 ± 0.16
-
106 44Ru
4.188 ± 0.092
4.13 ± 0.24
-
106 45Rh
4.188 ± 0.092
4.13 ± 0.24
-
121m 50Sn
0.0052 ± 0.0011
0.0053 ± 0.0012
-
122 51Sb
0.000024 ± 0.0000063
0.0000153 ± 0.000005
-
124 51Sb
0.00228 ± 0.00049
0.00154 ± 0.00043
-
125 51Sb
0.117 ± 0.015
0.138 ± 0.022
-
132 52Te
5.095 ± 0.094
4.92 ± 0.32
-
129 53I
1.407 ± 0.086
1.31 ± 0.13
-
131 53I
3.724 ± 0.078
4.09 ± 0.12
-
133 53I
6.97 ± 0.13
6.99 ± 0.33
-
135 53I
6.33 ± 0.23
6.24 ± 0.22
-
128 54Xe
0.00000234 ± 0.00000085
0.0000025 ± 0.0000012
-
130 54Xe
0.00166 ± 0.00056
0.00231 ± 0.00085
-
131m 54Xe
0.0405 ± 0.004
0.0444 ± 0.0044
-
133 54Xe
6.99 ± 0.13
7.03 ± 0.33
-
133m 54Xe
0.216 ± 0.016
0.223 ± 0.021
-
135 54Xe
7.36 ± 0.24
7.5 ± 0.23
-
135m 54Xe
1.78 ± 0.21
1.97 ± 0.25
-
134 55Cs
0.00067 ± 0.00018
0.00115 ± 0.0003
-
137 55Cs
6.588 ± 0.08
6.35 ± 0.12
-
140 56Ba
5.322 ± 0.059
5.303 ± 0.074
-
140 57La
5.333 ± 0.059
5.324 ± 0.075
-
141 58Ce
5.205 ± 0.073
5.01 ± 0.16
-
144 58Ce
3.755 ± 0.03
3.504 ± 0.053
-
144 59Pr
3.756 ± 0.03
3.505 ± 0.053
-
142 60Nd
0.00000145 ± 0.0000004
0.00000251 ± 0.00000072
-
144 60Nd
3.756 ± 0.03
3.505 ± 0.053
-
147 60Nd
2.044 ± 0.039
1.929 ± 0.046
-
147 61Pm
2.044 ± 0.039
1.929 ± 0.046
-
148 61Pm
0.0000056 ± 0.0000019
0.000012 ± 0.000004
-
148m 61Pm
0.0000118 ± 0.0000044
0.000029 ± 0.000011
-
149 61Pm
1.263 ± 0.032
1.275 ± 0.056
-
151 61Pm
0.776 ± 0.018
0.796 ± 0.037
-
148 62Sm
0.0000168 ± 0.0000046
0.000039 ± 0.000011
-
150 62Sm
0.00227 ± 0.00078
0.0051 ± 0.0019
-
151 62Sm
0.776 ± 0.018
0.797 ± 0.037
-
153 62Sm
0.38 ± 0.03
0.4 ± 0.18
-
151 63Eu
0.776 ± 0.018
0.797 ± 0.037
-
152 63Eu
0.000000195 ± 0.00000005
0.00000048 ± 0.00000014
-
154 63Eu
0.000049 ± 0.000012
0.000127 ± 0.000043
-
155 63Eu
0.174 ± 0.03
0.171 ± 0.054
-
JEFF-3.1
Joint Evaluated Fission and Fusion File, Incident-neutron data,
http://www-nds.iaea.org/exfor/endf00.htm, 2 October 2006;
see also A. Koning, R. Forrest, M. Kellett, R. Mills, H. Henriksson,
Y. Rugama, The JEFF-3.1 Nuclear Data Library, JEFF Report 21,
OECD/NEA, Paris, France, 2006, ISBN92-64-02314-3.
Ordered by mass number
Decays, even if lengthy, are given down to the stable nuclide.
Decays with half lives longer than a century are marked with a single asterisk (*), while decays with a half life longer than a hundred million years are marked with two asterisks (**).
Neutron capture converts a few percent of nonradioactive 133Cs to 134Cs, which has very low direct yield because beta decay stops at 134Xe; further capture will add to long-lived 135Cs.
^Purkayastha, B. C., and G. R. Martin. "The yields of 129I in natural and in neutron-induced fission of uranium." Canadian Journal of Chemistry 34.3 (1956): 293-300.
^ abcdeM.-M. Bé, V. Chisté, C. Dulieu, E. Browne, V. Chechev, N. Kuzmenko, R. Helmer, A. Nichols,
E. Schönfeld, R. Dersch, Monographie BIPM-5, Table of Radionuclides, Vol. 2 - A = 151 to 242, 2004.
^ abcdefghijklmnM.-M. Bé, V.P. Chechev, R. Dersch, O.A.M. Helene, R.G. Helmer, M. Herman, S. Hlavác,
A. Marcinkowski, G.L. Molnár, A.L. Nichols, E. Schönfeld, V.R. Vanin, M.J. Woods, IAEA CRP "Update of X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other Applications", IAEA Scientific and Technical Information report STI/PUB/1287, May 2007, International Atomic Energy Agency, Vienna, Austria, ISBN92-0-113606-4.