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Fission product yield

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:

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, while chain yields do not change after completion of neutron emission by a few neutron-rich initial fission products (delayed neutrons), with halflife 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%.

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.

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 gives yields for notable radioactive (with halflife 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 halflife 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 halflife 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 nonradioactive ¹³⁶Xe, rather than decaying to ¹³⁵Cs which is radioactive with a halflife of 2.3 million years
Nonradioactive ¹³³Cs capturing a neutron and becoming ¹³⁴Cs which is radioactive with a halflife of 2 years
Many of the fission products with mass 147 or greater such as Promethium-147, Samarium-149, Samarium-151, Europium-155 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
activation products of neutron capture by the reactor or bomb structure or the environment

Ordered by yield (thermal neutron fission of U-235)

Yield	Isotope	Halflife	Comment
6.7896%	¹³³Cs → ¹³⁴Cs	2.065y	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%	¹³⁵I → ¹³⁵Xe	6.57h	most important neutron poison; neutron capture converts 10%-50% of ¹³⁵Xe to ¹³⁶Xe; remainder decays (9.14h) to ¹³⁵Cs (2.3my)
6.2956%	⁹³Zr	1.53my
6.0899%	¹³⁷Cs	30.17y
6.0507%	⁹⁹Tc	211ky	Candidate for disposal by nuclear transmutation
5.7518%	⁹⁰Sr	28.9y
2.8336%	¹³¹I	8.02d
2.2713%	¹⁴⁷Pm	2.62y
1.0888%	¹⁴⁹Sm	nonradioactive	2nd most significant neutron poison
0.6576%	¹²⁹I	15.7my	Candidate for disposal by nuclear transmutation
0.4203%	¹⁵¹Sm	90y	neutron poison; most will be converted to stable ¹⁵²Sm
0.3912%	¹⁰⁶Ru	373.6d
0.2717%	⁸⁵Kr	10.78y
0.1629%	¹⁰⁷Pd	6.5my
0.0508%	⁷⁹Se	295ky
0.0330%	¹⁵⁵Eu → ¹⁵⁵Gd	4.76y	both neutron poisons, most will be destroyed while fuel still in use
0.0297%	¹²⁵Sb	2.76y
0.0236%	¹²⁶Sn	230ky
0.0065%	¹⁵⁷Gd	nonradioactive	neutron poison
0.0003%	^113mCd	14.1y	neutron poison, most will be destroyed while fuel still in use

Ordered by mass number

Yield	Isotope
0.0508%	selenium-79
0.2717%	krypton-85
5.7518%	strontium-90
6.2956%	zirconium-93
6.0507%	technetium-99
0.3912%	ruthenium-106
0.1629%	palladium-107
0.0003%	cadmium-113m
0.0297%	antimony-125
0.0236%	tin-126
0.6576%	iodine-129
2.8336%	iodine-131
6.7896%	caesium-133 →	caesium-134
6.3333%	iodine-135 →	xenon-135 →	caesium-135
6.0899%	caesium-137
2.2713%	promethium-147
1.0888%	samarium-149
0.4203%	samarium-151
0.0330%	europium-155 →	gadolinium-155
0.0065%	gadolinium-157

Ordered by halflife

Yield	Isotope	Halflife	Comment
2.8336%	¹³¹I	8.02d	Important in nuclear explosions and accidents but not in cooled spent nuclear fuel
0.3912%	¹⁰⁶Ru	373.6d
6.7896%	¹³³Cs → ¹³⁴Cs	2.065y	neutron capture converts a few percent of nonradioactive ¹³³Cs to ¹³⁴Cs, which has low direct yield because beta decay stops at ¹³⁴Xe
2.2713%	¹⁴⁷Pm	2.62y
0.0297%	¹²⁵Sb	2.76y
<0.0330%	¹⁵⁵Eu → ¹⁵⁵Gd	4.76y	both neutron poisons, most will be destroyed by neutron capture while still in reactor
0.2717%	⁸⁵Kr	10.78y	Current nuclear reprocessing releases it to atmosphere
<0.0003%	^113mCd	14.1y	most will be destroyed by neutron capture while still in reactor
5.7518%	⁹⁰Sr	28.9y	One of two principal medium-term radiation and heat sources
6.0899%	¹³⁷Cs	30.17y	One of two principal medium-term radiation and heat sources
<0.4203%	¹⁵¹Sm	90y	Most will be destroyed by neutron capture while still in reactor
6.0507%	⁹⁹Tc	211ky	Dominant radiation source among FP in period about to years; mobile in environment; candidate for disposal by nuclear transmutation
0.0236%	¹²⁶Sn	230ky
0.0508%	⁷⁹Se	295ky
6.2956%	⁹³Zr	1.53my
<6.3333%	¹³⁵Cs	2.3my
0.1629%	¹⁰⁷Pd	6.5my
0.6576%	¹²⁹I	15.7my	Mobile in environment; candidate for disposal by nuclear transmutation
<1.0888%	¹⁴⁹Sm	nonradioactive	neutron poison
<0.0065%	¹⁵⁷Gd	nonradioactive	neutron poison

Ordered by thermal neutron neutron absorption cross section

Barns	Yield	Isotope	t_½	Comment
2650000	6.3333%	¹³⁵I → ¹³⁵Xe	6.57h	Most important neutron poison; neutron capture rapidly converts ¹³⁵Xe to ¹³⁶Xe; remainder decays (9.14h) to ¹³⁵Cs (2.3my)
254000	0.0065%	¹⁵⁷Gd	∞	neutron poison, but low yield
40140	1.0888%	¹⁴⁹Sm	∞	2nd most important neutron poison
20600	0.0003%	^113mCd	14.1y	most will be destroyed by neutron capture
15200	0.4203%	¹⁵¹Sm	90y	most will be destroyed by neutron capture
3950	0.0330%	¹⁵⁵Eu → ¹⁵⁵Gd	4.76y	both neutron poisons
96	2.2713%	¹⁴⁷Pm	2.62y
80	2.8336%	¹³¹I	8.02d
29 140	6.7896%	¹³³Cs → ¹³⁴Cs	∞ 2.065y	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
20	6.0507%	⁹⁹Tc	211ky	candidate for disposal by nuclear transmutation
18	0.6576%	¹²⁹I	15.7my	candidate for disposal by nuclear transmutation
2.7	6.2956%	⁹³Zr	1.53my	transmutation impractical
1.8	0.1629%	¹⁰⁷Pd	6.5my
1.66	0.2717%	⁸⁵Kr	10.78y
0.90	5.7518%	⁹⁰Sr	28.9y
0.15	0.3912%	¹⁰⁶Ru	373.6d
0.11	6.0899%	¹³⁷Cs	30.17y
	0.0297%	¹²⁵Sb	2.76y
	0.0236%	¹²⁶Sn	230ky
	0.0508%	⁷⁹Se	295ky