In nuclear physics, fission product yield refers to the fraction of a fission product produced per fission. Nuclear fission splits a heavy nucleus such as uranium or plutonium into two lighter nuclei, which are called fission products.
Yield can be broken down by: Individual isotope Chemical element spanning several isotopes of different mass number but same atomic number. 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. In contrast, 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 one 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%).
Definitions There are several types of yields. For the most common fission reactions, the decay of the fission products preserve mass number. Thus the products form decay chains of constant mass. That makes the independent yield especially useful.Mills, R. W. (1995). Fission product yield evaluation (Doctoral dissertation, University of Birmingham).
The independent yield is a product of three factors, Y(A) the sum yield or mass yield, the fractional independent yield, and R(A,Z,I) the isomeric yield ratio:
Here possible product of fission can be represented by a triplet (A,Z,I), where A is the mass number, Z is the atomic number, and I is an integer for isomeric excited state, numbered from 0 for the ground state. For each decay chain (mass number A) the fractional independent yields and isomeric yield formulas sum to one:
and the independent yields sum to the sum yield for each chain:
The independent yield excludes delayed neutron emission. The cumulative yield,, c(A,Z,I), of a nuclide (A,Z,I) is the total number of atoms produced by one fission over all time. The chain yield, Ch(A), is the sum of all the cumulative yields for one mass chain for one fission. The independent, cumulative, and chain yields are given as percent per fission, that is as the yield of products per 100 fission reaction.
Examples The main fission products can be distinguished based on their lifetime: medium- or long-lived fission products, as presented in the two tables below.
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, as nuclei closer to magic numbers are more stable.
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 .
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% 200,000 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
plutonium containing 238Pu, 239Pu, 240Pu, 241Pu, and 242Pu, minor actinides including 237Np, 241Am, 243Am, curium isotopes, and perhaps californium reprocessed uranium containing 236U and other isotopes tritium, mostly from ternary fission or as an activation product in heavy water reactors activation products of neutron capture by the reactor or bomb structure or the environment Helium-4 from alpha decay
Fission products from U-235 + Yield Element Isotope Halflife Comment 6.7896% Caesium 133Cs → 134Cs 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% Iodine, xenon 135I → 135Xe 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% Zirconium 93Zr 1.53 My Long-lived fission product also produced by neutron activation in zircalloy cladding. 6.1% Molybdenum 99Mo 65.94 h Its daughter nuclide 99mTc is important in medical diagnosing. 6.0899% Caesium 137Cs 30.17 y Source of most of the decay heat from years to decades after irradiation, together with . 6.0507% Technetium 99Tc 211 ky Candidate for disposal by nuclear transmutation. 5.7518% Strontium 90Sr 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% Iodine 131I 8.02 d Reason for the use of potassium iodide tablets after nuclear accidents or nuclear bomb explosions. 2.2713% Promethium 147Pm 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% Samarium 149Sm Observationally stable 2nd most significant neutron poison. 0.9%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. Iodine 129I 15.7 My Long-lived fission product. Candidate for disposal by nuclear transmutation. 0.4203% Samarium 151Sm 90 y Neutron poison; most will be converted to stable 152Sm. 0.3912% Ruthenium 106Ru 373.6 d ruthenium tetroxide is volatile and chemically aggressive; daughter nuclide decays quickly to stable 0.2717% Krypton 85Kr 10.78 y noble gas; has some uses in industry to detect fine cracks in materials via autoradiography 0.1629% Palladium 107Pd 6.5 My Long-lived fission product; hampers extraction of stable isotopes of platinum group metals for use due to chemical similarity. 0.0508% Selenium 79Se 327 ky 0.0330% Europium, gadolinium 155Eu → 155Gd 4.76 y Both neutron poisons, most will be destroyed while fuel still in use. 0.0297% Antimony 125Sb 2.76 y 0.0236% Tin 126Sn 230 ky 0.0065% Gadolinium 157Gd stable Neutron poison. 0.0003% Cadmium 113mCd 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 (%) Product Thermal fission yield Fast fission yield 14-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