Fission product yield explained

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.

Yield can be broken down by:

  1. Individual isotope
  2. Chemical element spanning several isotopes of different mass number but same atomic number.
  3. Nuclei of a given mass number regardless of atomic number. Known as "chain yield" because it represents a decay chain of beta decay.

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 greater is stable and does not 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 table in the next section ("Ordered by yield") gives yields for notable radioactive (with half-lives greater than one year, plus iodine-131) fission products, and (the few most absorptive) neutron poison fission products, from thermal neutron fission of U-235 (typical of nuclear power reactors), computed from http://books.elsevier.com/companions/075067136X/pdfs/Yield.bas?mscssid=HAX80JCKT7RB8LS6F675GU2LM83N1CL6.

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.:

Besides fission products, the other types of radioactive products are

Fission products from U-235

Yield Element Isotope Halflife Comment
6.7896% 2.065 y 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.
6.3333% 6.57 h Most important neutron poison; neutron capture converts 10–50% of 135Xe to 136Xe; remainder decays (9.14h) to 135Cs (2.3 My).
6.2956% 1.53 My Long-lived fission product also produced by neutron activation in zircalloy cladding.
6.1% 65.94 h Its daughter nuclide 99mTc is important in medical diagnosing.
6.0899% 30.17 y Source of most of the decay heat from years to decades after irradiation, together with .
6.0507% 211 ky Candidate for disposal by nuclear transmutation.
5.7518% 28.9 y Source of much of the decay heat together with on the timespan of years to decades after irradiation. Formerly used in radioisotope thermoelectric generators.
2.8336% 8.02 d Reason for the use of potassium iodide tablets after nuclear accidents or nuclear bomb explosions.
2.2713% 2.62 y beta decays to very long lived Samarium-147 (half life>age of the universe); has seen some use in radioisotope thermoelectric generators
1.0888% Observationally stable 2nd most significant neutron poison.
0.9%[3] 15.7 My Long-lived fission product. Candidate for disposal by nuclear transmutation.
0.4203% 90 y Neutron poison
most will be converted to stable 152Sm.
0.3912% 373.6 druthenium tetroxide is volatile and chemically aggressive; daughter nuclide decays quickly to stable
0.2717% 10.78 y noble gas
has some uses in industry to detect fine cracks in materials via autoradiography
0.1629% 6.5 My Long-lived fission product
hampers extraction of stable isotopes of platinum group metals for use due to chemical similarity.
0.0508% 327 ky
0.0330% 4.76 y Both neutron poisons, most will be destroyed while fuel still in use.
0.0297% 2.76 y
0.0236% 230 ky
0.0065% stable Neutron poison.
0.0003% 14.1 y 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]
ProductThermal fission yieldFast fission yield14-MeV fission yield
0.00171 ± 0.00018 0.00269 ± 0.00044 0.00264 ± 0.00045
0.00084 ± 0.00015 0.00082 ± 0.00012 0.00081 ± 0.00012
0.0108 ± 0.0004 0.0108 ± 0.0004 0.0174 ± 0.0036
0.0108 ± 0.0004 0.0108 ± 0.0004 0.0174 ± 0.0036
0.1702 ± 0.0049 0.17 ± 0.0049 0.1667 ± 0.0088
1.304 ± 0.012 1.309 ± 0.043 1.64 ± 0.31
0.000285 ± 0.000076 0.00044 ± 0.00016 0.038 ± 0.012
0.286 ± 0.021 0.286 ± 0.026 0.47 ± 0.1
1.303 ± 0.012 1.307 ± 0.043 1.65 ± 0.31
5.73 ± 0.13 5.22 ± 0.18 4.41 ± 0.18
6.502 ± 0.072 6.349 ± 0.083 5.07 ± 0.19
0.00000042 ± 0.00000011 2.90±0.770 × 10−8 0.00004 ± 0.000015
6.498 ± 0.072 6.345 ± 0.083 5.07 ± 0.19
0.0702 ± 0.0067 0.0686 ± 0.0071 0.0548 ± 0.0072
0 ± 0 0 ± 0 0 ± 0
8.70 × 10−10 ± 3.20 × 10−10 0 ± 0 6.20 × 10−8 ± 2.50 × 10−8
0.00042 ± 0.00015 0.000069 ± 0.000025 0.0033 ± 0.0015
6.132 ± 0.092 5.8 ± 0.13 5.02 ± 0.13
6.132 ± 0.092 5.8 ± 0.13 5.02 ± 0.13
3.103 ± 0.084 3.248 ± 0.042 3.14 ± 0.11
0.41 ± 0.011 0.469 ± 0.036 2.15 ± 0.59
0.41 ± 0.011 0.469 ± 0.036 2.15 ± 0.59
0.00106 ± 0.00011 0.0039 ± 0.00091 0.142 ± 0.023
0.000000366 ± 0.000000098 0.0000004 ± 0.00000014 0.00193 ± 0.00068
0.000089 ± 0.000021 0.000112 ± 0.000034 0.027 ± 0.01
0.026 ± 0.0014 0.067 ± 0.011 1.42 ± 0.42
4.276 ± 0.043 4.639 ± 0.065 3.85 ± 0.16
0.706 ± 0.032 1.03 ± 0.26 1.59 ± 0.18
2.878 ± 0.032 3.365 ± 0.054 4.11 ± 0.14
6.59 ± 0.11 6.61 ± 0.13 5.42 ± 0.4
6.39 ± 0.22 6.01 ± 0.18 4.8 ± 1.4
0 ± 0 0 ± 0 0.00108 ± 0.00048
0.000038 ± 0.0000098 0.000152 ± 0.000055 0.038 ± 0.014
0.0313 ± 0.003 0.0365 ± 0.0031 0.047 ± 0.0049
6.6 ± 0.11 6.61 ± 0.13 5.57 ± 0.41
0.189 ± 0.015 0.19 ± 0.015 0.281 ± 0.049
6.61 ± 0.22 6.32 ± 0.18 6.4 ± 1.8
1.22 ± 0.12 1.23 ± 0.13 2.17 ± 0.66
0.0000121 ± 0.0000032 0.0000279 ± 0.0000073 0.0132 ± 0.0035
6.221 ± 0.069 5.889 ± 0.096 5.6 ± 1.3
6.314 ± 0.095 5.959 ± 0.048 4.474 ± 0.081
6.315 ± 0.095 5.96 ± 0.048 4.508 ± 0.081
5.86 ± 0.15 5.795 ± 0.081 4.44 ± 0.2
5.474 ± 0.055 5.094 ± 0.076 3.154 ± 0.038
5.474 ± 0.055 5.094 ± 0.076 3.155 ± 0.038
6.30 × 10−9 ± 1.70 × 10−9 1.70 × 10−9 ± 4.80 × 10−10 0.0000137 ± 0.0000049
5.475 ± 0.055 5.094 ± 0.076 3.155 ± 0.038
2.232 ± 0.04 2.148 ± 0.028 1.657 ± 0.045
2.232 ± 0.04 2.148 ± 0.028 1.657 ± 0.045
5.00 × 10−8 ± 1.70 × 10−8 7.40 × 10−9 ± 2.50 × 10−9 0.0000013 ± 0.00000042
0.000000104 ± 0.000000039 1.78 × 10−8 ± 6.60 × 10−9 0.0000048 ± 0.0000018
1.053 ± 0.021 1.064 ± 0.03 0.557 ± 0.09
0.4204 ± 0.0071 0.431 ± 0.015 0.388 ± 0.061
0.000000149 ± 0.000000041 2.43 × 10−8 ± 6.80 × 10−9 0.0000058 ± 0.0000018
0.000061 ± 0.000022 0.0000201 ± 0.0000077 0.00045 ± 0.00018
0.4204 ± 0.0071 0.431 ± 0.015 0.388 ± 0.061
0.1477 ± 0.0071 0.1512 ± 0.0097 0.23 ± 0.015
0.4204 ± 0.0071 0.431 ± 0.015 0.388 ± 0.061
3.24 × 10−10 ± 8.50 × 10−11 0 ± 0 3.30 × 10−8 ± 1.10 × 10−8
0.000000195 ± 0.000000064 4.00 × 10−8 ± 1.10 × 10−8 0.0000033 ± 0.0000011
0.0308 ± 0.0013 0.044 ± 0.01 0.088 ± 0.014
+ Cumulative fission yield per fission for Pu-239 (%)
ProductThermal fission yieldFast fission yield14-MeV fission yield
0.00408 ± 0.00041 0.00346 ± 0.00057 -
0.00135 ± 0.00019 0.00106 ± 0.00016 -
0.0142 ± 0.0007 0.0142 ± 0.0007 -
0.0142 ± 0.0007 0.0142 ± 0.0007 -
0.2192 ± 0.009 0.219 ± 0.009 -
0.574 ± 0.026 0.617 ± 0.049 -
0.00175 ± 0.0006 0.00055 ± 0.0002 -
0.136 ± 0.014 0.138 ± 0.017 -
0.576 ± 0.026 0.617 ± 0.049 -
2.013 ± 0.054 2.031 ± 0.057 -
4.949 ± 0.099 4.682 ± 0.098 -
0.0000168 ± 0.0000045 0.00000255 ± 0.00000069 -
4.946 ± 0.099 4.68 ± 0.098 -
0.0535 ± 0.0066 0.0506 ± 0.0062 -
0 ± 0 0 ± 0 -
3.60 × 10−8 ± 1.30 × 10−8 4.80 × 10−9 ± 1.70 × 10−9 -
0.0051 ± 0.0018 0.0017 ± 0.00062 -
6.185 ± 0.056 5.82 ± 0.13 -
6.184 ± 0.056 5.82 ± 0.13 -
6.948 ± 0.083 6.59 ± 0.16 -
4.188 ± 0.092 4.13 ± 0.24 -
4.188 ± 0.092 4.13 ± 0.24 -
0.0052 ± 0.0011 0.0053 ± 0.0012 -
0.000024 ± 0.0000063 0.0000153 ± 0.000005 -
0.00228 ± 0.00049 0.00154 ± 0.00043 -
0.117 ± 0.015 0.138 ± 0.022 -
5.095 ± 0.094 4.92 ± 0.32 -
1.407 ± 0.086 1.31 ± 0.13 -
3.724 ± 0.078 4.09 ± 0.12 -
6.97 ± 0.13 6.99 ± 0.33 -
6.33 ± 0.23 6.24 ± 0.22 -
0.00000234 ± 0.00000085 0.0000025 ± 0.0000012 -
0.00166 ± 0.00056 0.00231 ± 0.00085 -
0.0405 ± 0.004 0.0444 ± 0.0044 -
6.99 ± 0.13 7.03 ± 0.33 -
0.216 ± 0.016 0.223 ± 0.021 -
7.36 ± 0.24 7.5 ± 0.23 -
1.78 ± 0.21 1.97 ± 0.25 -
0.00067 ± 0.00018 0.00115 ± 0.0003 -
6.588 ± 0.08 6.35 ± 0.12 -
5.322 ± 0.059 5.303 ± 0.074 -
5.333 ± 0.059 5.324 ± 0.075 -
5.205 ± 0.073 5.01 ± 0.16 -
3.755 ± 0.03 3.504 ± 0.053 -
3.756 ± 0.03 3.505 ± 0.053 -
0.00000145 ± 0.0000004 0.00000251 ± 0.00000072 -
3.756 ± 0.03 3.505 ± 0.053 -
2.044 ± 0.039 1.929 ± 0.046 -
2.044 ± 0.039 1.929 ± 0.046 -
0.0000056 ± 0.0000019 0.000012 ± 0.000004 -
0.0000118 ± 0.0000044 0.000029 ± 0.000011 -
1.263 ± 0.032 1.275 ± 0.056 -
0.776 ± 0.018 0.796 ± 0.037 -
0.0000168 ± 0.0000046 0.000039 ± 0.000011 -
0.00227 ± 0.00078 0.0051 ± 0.0019 -
0.776 ± 0.018 0.797 ± 0.037 -
0.38 ± 0.03 0.4 ± 0.18 -
0.776 ± 0.018 0.797 ± 0.037 -
0.000000195 ± 0.00000005 0.00000048 ± 0.00000014 -
0.000049 ± 0.000012 0.000127 ± 0.000043 -
0.174 ± 0.03 0.171 ± 0.054 -
JEFF-3.1Joint 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, .

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 .

Yield Isotope
0.0508% selenium-79bromine-79
0.2717% rubidium-85
5.7518% zirconium-90
6.2956% zirconium-93 * niobium-93
6.0507% technetium-99ruthenium-99
0.3912% palladium-106
0.1629% palladium-107silver-107
0.0003% cadmium-113 (essentially stable)** indium-113
0.0297% tellurium-125
0.0236% tin-126 * tellurium-126
0.9% iodine-129xenon-129
2.8336% xenon-131
6.7896% barium-134
6.3333% caesium-135barium-135
6.3333% xenon-136 (essentially stable)** barium-136
6.0899% barium-137
2.2713% samarium-147neodymium-143
1.0888% samarium-149
0.4203% samarium-151
0.0330% gadolinium-155
0.0065% gadolinium-157

Half lives, decay modes, and branching fractions

Half-lives and decay branching fractions for fission products[5]
Nuclide Half-life Decay mode Branching fraction Source Notes
2.9 ± 0.06 m β 1.0 [6]
10.752 ± 0.023 y β 1.0 [7]
4.48 ± 0.008 h IT 0.214 ± 0.005
β 0.786 ± 0.005
28.8 ± 0.07 y β 1.0 [8]
64.032 ± 0.006 d β 1.0
(7.3 ± 0.9) × 106 d β 1.0 [9]
3.61 ± 0.03 d β 0.025 ± 0.001
IT 0.975 ± 0.001
34.985 ± 0.012 d β 1.0
(2.111 ± 0.012) × 105 y β 1.0
39.247 ± 0.013 d β 1.0
1.018 ± 0.005 y β 1.0
30.1 ± 0.3 s β 1.0
55 ± 5 y β 0.224 ± 0.02
IT 0.776 ± 0.02
2.7238 ± 0.0002 d EC 0.0241 ± 0.0012
β 0.9759 ± 0.0012
60.2 ± 0.03 d β 1.0
2.7584 ± 0.0006 y β 1.0
(5.89 ± 0.23) × 109 d β 1.0
8.0233 ± 0.0019 d β 1.0
20.87 ± 0.08 h β 1.0
6.57 ± 0.02 h β 1.0
11.930 ± 0.016 d IT 1.0
5.243 ± 0.001 d β 1.0
2.19 ± 0.01 d IT 1.0
9.14 ± 0.02 h β 1.0
15.29 ± 0.05 m β 0.003 ± 0.003
IT 0.997 ± 0.003
2.063 ± 0.003 y EC 0.000003 ± 0.000001
β 0.999997 ± 0.000001
30.05 ± 0.08 y β 1.0
12.753 ± 0.004 d β 1.0
1.67850 ± 0.00017 d β 1.0
32.508 ± 0.010 d β 1.0
285.1 ± 0.6 d β 1.0
17.28 ± 0.05 m β 1.0
10.98 ± 0.01 d β 1.0
2.6234 ± 0.0002 y β 1.0
41.29 ± 0.11 d IT 0.042 ± 0.007
β 0.958 ± 0.007
5.368 ± 0.002 d β 1.0
2.2117 ± 0.0021 d β 1.0
1.1833 ± 0.0017 d β 1.0
90 ± 6 y β 1.0
1.938 ± 0.010 d β 1.0
(4.941 ± 0.007) × 103 d β 0.279 ± 0.003
EC 0.721 ± 0.003
(3.1381 ± 0.0014) × 103 d EC 0.00018 ± 0.00013
β 0.99982 ± 0.00013
4.753 ± 0.016 y β 1.0

Ordered by thermal neutron absorption cross section

Barns Yield Isotope t½ Comment
6.3333% 6.57 h Most important neutron poison; neutron capture rapidly converts 135Xe to 136Xe; remainder decays (9.14 h) to 135Cs (2.3 My).
0.0065% Neutron poison, but low yield.
1.0888% 2nd most important neutron poison.
0.0003% 14.1 y Most will be destroyed by neutron capture.
0.4203% 90 y Most will be destroyed by neutron capture.

60,900
0.0330% 4.76 y Both neutron poisons.
2.2713% 2.62 ySuitable for radioisotope thermoelectric generators with annual or semi-annual refueling.
2.8336% 8.02 d

140
6.7896%
2.065 y
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.
6.0507% 211 ky Candidate for disposal by nuclear transmutation.
0.6576% 15.7 My Candidate for disposal by nuclear transmutation.
6.2956% 1.53 My Transmutation impractical.
0.1629% 6.5 My
0.2717% 10.78 y
5.7518% 28.9 y
0.3912% 373.6 d
6.0899% 30.17 y
0.0297% 2.76 y
0.0236% 230 ky
0.0508% 327 ky

References

  1. Web site: fissionyield . 2007-06-10 . https://web.archive.org/web/20070528055359/http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/fissionyield.html . 2007-05-28 . dead .
  2. Nuclear fission modes and fragment mass asymmetries in a five-dimensional deformation space. Nature. 15 February 2001. 409. 6822. 785–790. 10.1038/35057204. 11236985 . Möller . P . Madland . DG . Sierk . AJ . Iwamoto . A. 2001Natur.409..785M. 9754793.
  3. 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.
  4. Web site: Cumulative Fission Yields . www-nds.iaea.org. IAEA. 11 November 2016.
  5. Web site: Half-lives and decay branching fractions for activation products . www-nds.iaea.org . IAEA . 11 November 2016.
  6. Evaluated Nuclear Structure Data File, http://www-nds.iaea.org/ensdf/, 26 January 2006.
  7. M.-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.
  8. Laboratoire National Henri Becquerel, Recommended Data, http://www.nucleide.org/DDEP_WG/DDEPdata.htm, 16 January 2006.
  9. M.-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, .

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