fission product yield

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).{{rp|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:

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

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:

$$\backslash Sigma\_Z\; f(A,Z)\; =\; \backslash Sigma\_I\; R(A,Z,I)\; =\; 1$$

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

$$\backslash textrm\{Y\}(A)\; =\; \backslash Sigma\_\{Z,I\}\; \backslash textrm\{y\}(A,Z,I).$$

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.

Image:ThermalFissionYield.svg]]

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,{{Cite web |url=http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/fissionyield.html |title=fissionyield |access-date=2007-06-10 |archive-url=https://web.archive.org/web/20070528055359/http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/fissionyield.html |archive-date=2007-05-28 |url-status=dead }} as nuclei closer to magic numbers are more stable.{{cite journal|title=Nuclear fission modes and fragment mass asymmetries in a five-dimensional deformation space|journal=Nature|date=15 February 2001|volume=409|issue=6822|pages=785–790|doi=10.1038/35057204|pmid=11236985 | last1 = Möller | first1 = P | last2 = Madland | first2 = DG | last3 = Sierk | first3 = AJ | last4 = Iwamoto | first4 = A|bibcode=2001Natur.409..785M|s2cid=9754793|url=https://zenodo.org/record/1233095}}

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).

File:Fission yield volatile 2.png, 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 ("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]{{Dead link|date=December 2019 |bot=InternetArchiveBot |fix-attempted=yes }}.

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
• activation products of neutron capture by the reactor or bomb structure or the environment

Image:fission yield.png, probably of Pu-239 not U-235 because left hump is shifted right, 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.]]

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

Image:fission yield.png, probably of Pu-239 not U-235 because left hump is shifted right, 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.]]

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 ({{asterisk}}), while decays with a half life longer than a hundred million years are marked with two asterisks ({{asterisk}}{{asterisk}}).

{{noteslist}}

• [https://www-nds.iaea.org/sgnucdat/safeg2008.pdf HANDBOOK OF NUCLEAR DATA FOR SAFEGUARDS: DATABASE EXTENSIONS, AUGUST 2008]
• Image:Ndslivechart.png [http://www-nds.iaea.org/livechart The Live Chart of Nuclides - IAEA ] Color-map of yields, and detailed data by click on a nuclide.

Category:Nuclear fission

Category:Nuclear chemistry