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:

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. 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,^[1] so that the total yield percentages sum to 200%.^{[citation needed]} Less often, it is stated as percentage of all fission products, so that the percentages sum to 100%.^{[citation needed]} Ternary fission, about 0.2–0.4% of fissions, also produces a third light nucleus such as helium-4 (90%) or tritium (7%).^{[citation needed]}

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.^[2]: 9

The independent yield is a product of three factors, Y(A) the sum yield or mass yield, f(A,Z) the fractional independent yield, and R(A,Z,I) the isomeric yield ratio:^[2]

\textrm{y}(A,Z,I) = \textrm{Y}(A)\cdot f(A,Z) \cdot R(A,Z,I)

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:

\Sigma_Z f(A,Z) = \Sigma_I R(A,Z,I) = 1

and the independent yields sum to the sum yield for each chain:

\textrm{Y}(A) = \Sigma_{Z,I} \textrm{y}(A,Z,I).

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.^[2]

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,^[3] as nuclei closer to magic numbers are more stable.^[4]

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 [1]^{[dead link]}.

The yields in the table sum to only 45.5522%, including 34.8401% which have half-lives greater than one year:

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.

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 (**).

Half lives, decay modes, and branching fractions

Ordered by thermal neutron absorption cross section

References

1. ^ IAEA. "Compilation and evaluation of fission yield nuclear data". www-pub.iaea.org. IAEA. Retrieved 12 December 2025.
2. ^ Mills, R. W. (1995). Fission product yield evaluation (Doctoral dissertation, University of Birmingham).
3. ^ "fissionyield". Archived from the original on 2007-05-28. Retrieved 2007-06-10.
4. ^ Möller, P; Madland, DG; Sierk, AJ; Iwamoto, A (15 February 2001). "Nuclear fission modes and fragment mass asymmetries in a five-dimensional deformation space". Nature. 409 (6822): 785–790. Bibcode:2001Natur.409..785M. doi:10.1038/35057204. PMID 11236985. S2CID 9754793
5. ^ 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.
6. ^ "Cumulative Fission Yields". www-nds.iaea.org. IAEA. Retrieved 11 November 2016.
7. ^ "Half-lives and decay branching fractions for activation products". www-nds.iaea.org. IAEA. Retrieved 11 November 2016.
8. ^ Evaluated Nuclear Structure Data File, http://www-nds.iaea.org/ensdf/, 26 January 2006.
9. ^ 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.
10. ^ Laboratoire National Henri Becquerel, Recommended Data, http://www.nucleide.org/DDEP_WG/DDEPdata.htm Archived 2021-02-13 at the Wayback Machine, 16 January 2006.
11. ^ 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, ISBN 92-0-113606-4.

External links

• Handbook of nuclear data for safeguards: Database extensions, August 2008
• The Live Chart of Nuclides – IAEA Color-map of yields, and detailed data by clicking on a nuclide.

1. ^ β⁻ decay branches of 0.9982 ± 0.0002 to Kr-85m and 0.0018 ± 0.0002 to Kr-85.
2. ^ ENSDF branching fractions: 0.944 ± 0.007 for IT and 0.056 ± 0.007 for β⁻.
3. ^ β⁻ decay branch of 0.0288 ± 0.0002 to Xe-133m.
4. ^ Branching fractions were averaged from ENSDF database.
5. ^ Branching fractions were adopted from ENSDF database.
6. ^ Branching fractions were adopted from LNHB data.