Fissile material

Chart of nuclides showing thermal neutron fission cross section values. Increased fissility of odd–neutron isotopes is apparent. Grey boxes represent uncharacterized isotopes.

In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of any energy. The predominant neutron energy may be typified by either slow neutrons (i.e., a thermal system) or fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives.

Fissile vs fissionable

According to the fissile rule, for a heavy element with 90 ≤ Z ≤ 100, its isotopes with 2 × Z − N = 43 ± 2, with few exceptions, are fissile (where N = number of neutrons and Z = number of protons).^{[1][2][note 1]}

"Fissile" is distinct from "fissionable." A nuclide capable of undergoing fission (even with a low probability) after capturing a high energy neutron is referred to as "fissionable." A fissionable nuclide that can be induced to fission with low-energy thermal neutrons with a high probability is referred to as "fissile."^[3] Although the terms were formerly synonymous, fissionable materials include also those (such as uranium-238) that can be fissioned only with high-energy neutrons. As a result, fissile materials (such as uranium-235) are a subset of fissionable materials.

Uranium-235 fissions with low-energy thermal neutrons because the binding energy resulting from the absorption of a neutron is greater than the critical energy required for fission; therefore uranium-235 is a fissile material. By contrast, the binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Consequently, uranium-238 is a fissionable material but not a fissile material.^[4]

An alternative definition defines fissile nuclides as those nuclides that can be made to undergo nuclear fission (i.e., are fissionable) and also produce neutrons from such fission that can sustain a nuclear chain reaction in the correct setting. Under this definition, the only nuclides that are fissionable are those nuclides that can be made to undergo nuclear fission but produce insufficient neutrons, in either energy or number, to sustain a nuclear chain reaction.^[5] As such, while all fissile isotopes are fissionable, not all fissionable isotopes are fissile. In the arms control context, particularly in proposals for a Fissile Material Cutoff Treaty, the term "fissile" is often used to describe materials that can be used in the fission primary of a nuclear weapon.^[6] These are materials that sustain an explosive fast nuclear fission chain reaction.

Under all definitions above, uranium-238 (238
U
) is fissionable, but because it cannot sustain a neutron chain reaction, it is not fissile. Neutrons produced by fission of 238
U
have lower energies than the original neutron (they behave as in an inelastic scattering), usually below 1 MeV (i.e., a speed of about 14,000 km/s), the fission threshold to cause subsequent fission of 238
U
, so fission of 238
U
does not sustain a nuclear chain reaction.

Fast fission of 238
U
in the secondary stage of a nuclear weapon contributes greatly to yield and to fallout. The fast fission of 238
U
also makes a significant contribution to the power output of some fast-neutron reactors.

Fissile nuclides

Actinides and fission products by half-life
Actinides[7] by decay chain				Half-life range (y)	Fission products of ^235U by yield[8]
4n	4n+1	4n+2	4n+3
						4.5–7%	0.04–1.25%	<0.001%
^228Ra^№				4–6	†		^155Eu^þ
^244Cm^ƒ	^241Pu^ƒ	^250Cf	^227Ac^№	10–29		^90Sr	^85Kr	^113mCd^þ
^232U^ƒ		^238Pu^ƒ№	^243Cm^ƒ	29–97		^137Cs	^151Sm^þ	^121mSn
^248Bk[9]	^249Cf^ƒ	^242mAm^ƒ		141–351	No fission products have a half-life in the range of 100–210 k years ...
	^241Am^ƒ		^251Cf^ƒ[10]	430–900
		^226Ra^№	^247Bk	1.3 k – 1.6 k
^240Pu^ƒ№	^229Th^№	^246Cm^ƒ	^243Am^ƒ	4.7 k – 7.4 k
	^245Cm^ƒ	^250Cm		8.3 k – 8.5 k
			^239Pu^ƒ№	24.1 k
		^230Th^№	^231Pa^№	32 k – 76 k
^236Np^ƒ	^233U^ƒ№	^234U^№		150 k – 250 k	‡	^99Tc^₡	^126Sn
^248Cm		^242Pu^ƒ		327 k – 375 k			^79Se^₡
				1.53 M		^93Zr
	^237Np^ƒ№			2.1 M – 6.5 M		^135Cs^₡	^107Pd
^236U^№			^247Cm^ƒ	15 M – 24 M			^129I^₡
^244Pu^№				80 M	... nor beyond 15.7 M years[11]
^232Th^№		^238U^№	^235U^ƒ№	0.7 G – 14.1 G
Legend for superscript symbols ₡  has thermal neutron capture cross section in the range of 8–50 barns ƒ  fissile m  metastable isomer №  naturally occurring radioactive material (NORM) þ  neutron poison (thermal neutron capture cross section greater than 3k barns) †  range 4–97 y: Medium-lived fission product ‡  over 200,000 y: Long-lived fission product

In general, most actinide isotopes with an odd neutron number are fissile. Most nuclear fuels have an odd atomic mass number (A = Z + N = the total number of nucleons), and an even atomic number Z. This implies an odd number of neutrons. Isotopes with an odd number of neutrons gain an extra 1 to 2 MeV of energy from absorbing an extra neutron, from the pairing effect which favors even numbers of both neutrons and protons. This energy is enough to supply the needed extra energy for fission by slower neutrons, which is important for making fissionable isotopes also fissile.

More generally, nuclides with an even number of protons and an even number of neutrons, and located near a well-known curve in nuclear physics of atomic number vs. atomic mass number are more stable than others; hence, they are less likely to undergo fission. They are more likely to "ignore" the neutron and let it go on its way, or else to absorb the neutron but without gaining enough energy from the process to deform the nucleus enough for it to fission. These "even-even" isotopes are also less likely to undergo spontaneous fission, and they also have relatively much longer partial half-lives for alpha or beta decay. Examples of these isotopes are uranium-238 and thorium-232. On the other hand, nuclei with an odd number of protons and an odd number of neutrons (odd Z, odd N) are usually short-lived (a notable exception is neptunium-236 with a half-life of 154,000 years) because they readily decay by beta-particle emission to their isobars with an even number of protons and an even number of neutrons (even Z, even N) becoming much more stable. The physical basis for this phenomenon also comes from the pairing effect in nuclear binding energy, but this time from both proton–proton and neutron–neutron pairing. The relatively short half-life of such odd-odd heavy isotopes means that they are not available in quantity and are highly radioactive.

Nuclear fuel

To be a useful fuel for nuclear fission chain reactions, the material must:

• Be in the region of the binding energy curve where a fission chain reaction is possible (i.e., above radium)
• Have a high probability of fission on neutron capture
• Release two or more neutrons on average per neutron capture (which means a higher average number of them on each fission, to compensate for nonfissions, and absorptions in the moderator)
• Have a reasonably long half-life
• Be available in suitable quantities

Capture-fission ratios of fissile nuclides

Thermal neutrons[12]				Epithermal neutrons
σF	σγ	%		σF	σγ	%
531	46	8.0%	^233U	760	140	16%
585	99	14.5%	^235U	275	140	34%
750	271	26.5%	^239Pu	300	200	40%
1010	361	26.3%	^241Pu	570	160	22%

Fissile nuclides in nuclear fuels include:

• Uranium-235 which occurs in natural uranium and enriched uranium
• Plutonium-239 bred from uranium-238 by neutron capture
• Plutonium-241 bred from plutonium-240 by neutron capture. The 240
  Pu
  comes from 239
  Pu
  by the same process.
• Uranium-233 bred from thorium-232 by neutron capture

Fissile nuclides do not have a 100% chance of undergoing fission on absorption of a neutron. The chance is dependent on the nuclide as well as neutron energy. For low and medium-energy neutrons, the neutron capture cross sections for fission (σ_F), the cross section for neutron capture with emission of a gamma ray (σ_γ), and the percentage of non-fissions are in the table at right.

See also

• Fertile material
• Fission product
• Special nuclear material

Notes

1. The fissile rule thus formulated indicates 33 isotopes as likely fissile: Th-225, 227, 229; Pa-228, 230, 232; U-231, 233, 235; Np-234, 236, 238; Pu-237, 239, 241; Am-240, 242, 244; Cm-243, 245, 247; Bk-246, 248, 250; Cf-249, 251, 253; Es-252, 254, 256; Fm-255, 257, 259. Only fourteen (including a long-lived metastable nuclear isomer) have half-lives of at least a year: Th-229, U-233, U-235, Np-236, Pu-239, Pu-241, Am-242m, Cm-243, Cm-245, Cm-247, Bk-248, Cf-249, Cf-251 and Es-252. Of these, only U-235 is naturally occurring. It is possible to breed U-233 and Pu-239 from more common naturally occurring isotopes (Th-232 and U-238 respectively) by single neutron capture. The others are typically produced in smaller quantities through further neutron absorption.

References

1. Ronen Y., 2006. A rule for determining fissile isotopes. Nucl. Sci. Eng., 152:3, pages 334-335.
2. Ronen, Y. (2010). "Some remarks on the fissile isotopes". Annals of Nuclear Energy. 37 (12): 1783–1784. doi:10.1016/j.anucene.2010.07.006.
3. "Slides-Part one: Kinetics". UNENE University Network of Excellence in Nuclear Engineering. Retrieved 3 January 2013.
4. James J. Duderstadt and Louis J. Hamilton (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0-471-22363-8.
5. John R. Lamarsh and Anthony John Baratta (Third Edition) (2001). Introduction to Nuclear Engineering. Prentice Hall. ISBN 0-201-82498-1.
6. Fissile Materials and Nuclear Weapons, International Panel on Fissile Materials
7. Plus radium (element 88). While actually a sub-actinide, it immediately precedes actinium (89) and follows a three-element gap of instability after polonium (84) where no isotopes have half-lives of at least four years (the longest-lived isotope in the gap is radon-222 with a half life of less than four days). Radium's longest lived isotope, at 1,600 years, thus merits the element's inclusion here.
8. Specifically from thermal neutron fission of U-235, e.g. in a typical nuclear reactor.
9. Milsted, J.; Friedman, A. M.; Stevens, C. M. (1965). "The alpha half-life of berkelium-247; a new long-lived isomer of berkelium-248". Nuclear Physics. 71 (2): 299. doi:10.1016/0029-5582(65)90719-4.
   "The isotopic analyses disclosed a species of mass 248 in constant abundance in three samples analysed over a period of about 10 months. This was ascribed to an isomer of Bk²⁴⁸ with a half-life greater than 9 y. No growth of Cf²⁴⁸ was detected, and a lower limit for the β⁻ half-life can be set at about 10⁴ y. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 y."
10. This is the heaviest isotope with a half-life of at least four years before the "Sea of Instability".
11. Excluding those "classically stable" isotopes with half-lives significantly in excess of ²³²Th; e.g., while ^113mCd has a half-life of only fourteen years, that of ¹¹³Cd is nearly eight quadrillion years.
12. "Interactive Chart of Nuclides". Brookhaven National Laboratory. Retrieved 2013-08-12.