Fission product yield

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, 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. Chain yields do not account for these "shadowed" isotopes; however, they have very low yields 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 or tritium.

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.
The independent yield is a product of three factors, Y the sum yield or mass yield, the fractional independent yield, and R the isomeric yield ratio:
Here possible product of fission can be represented by a triplet, 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 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, of a nuclide is the total number of atoms produced by one fission over all time. The chain yield, Ch, 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.
File:Fission yield volatile 2.png|thumb|450px|Yield vs Z. Colors indicate fluoride volatility, which is important in nuclear reprocessing: Blue elements have volatile fluorides or are already volatile; green elements do not but have volatile chlorides; red elements have neither, but the elements themselves are volatile at very high temperatures. Yields at 10^0,1,2,3 years after fission, not considering later neutron capture, fraction of 100% not 200%. Beta decay Kr-85→Rb, Sr-90→Zr, Ru-106→Pd, Sb-125→Te, Cs-137→Ba, Ce-144→Nd, Sm-151→Eu, Eu-155→Gd visible.
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 gives yields for notable radioactive fission products, and neutron poison fission products, from thermal neutron fission of U-235, computed from .
The yields in the table sum to only 45.5522%, including 34.8401% which have half-lives greater than one year:

t_½ 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

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

Cumulative fission yields

Cumulative fission yields give the amounts of nuclides produced either directly in the fission or by decay of other nuclides.

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

Product	Thermal fission yield	Fast fission yield	14-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-3.1

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,.

Fission product yield

Definitions

Examples

Mass vs. yield curve

Fission products from U-235

Cumulative fission yields