Fissile material
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 thermalneutron reactors, fastneutron reactors and nuclear explosives.
Fissile vs fissionable
According to the Ronen fissile rule,^{[1]} 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).^{[2]}^{[3]}^{[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 lowenergy thermal neutrons with a high probability is referred to as "fissile".^{[4]} Although the terms were formerly synonymous, fissionable materials include also those (such as uranium238) that can be fissioned only with highenergy neutrons. As a result, fissile materials (such as uranium235) are a subset of fissionable materials.
Uranium235 fissions with lowenergy thermal neutrons because the binding energy resulting from the absorption of a neutron is greater than the critical energy required for fission; therefore uranium235 is a fissile material. By contrast, the binding energy released by uranium238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Consequently, uranium238 is a fissionable material but not a fissile material.^{[5]}
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 but not fissile 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.^{[6]} 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.^{[7]} These are materials that sustain an explosive fast neutron nuclear fission chain reaction.
Under all definitions above, uranium238 (^{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 fastneutron reactors.
Fissile nuclides
Actinides and fission products by halflife



Actinides^{[8]} by decay chain 
Halflife range (y) 
Fission products of ^{235}U by yield^{[9]}  
4n  4n+1  4n+2  4n+3  
4.5–7%  0.04–1.25%  <0.001%  
^{228}Ra^{№}  4–6  †  ^{155}Eu^{þ}  
^{244}Cm^{ƒ}  ^{241}Pu^{ƒ}  ^{250}Cf  ^{227}Ac^{№}  10–29  ^{90}Sr  ^{85}Kr  ^{113m}Cd^{þ}  
^{232}U^{ƒ}  ^{238}Pu^{ƒ}  ^{243}Cm^{ƒ}  29–97  ^{137}Cs  ^{151}Sm^{þ}  ^{121m}Sn  
^{248}Bk^{[10]}  ^{249}Cf^{ƒ}  ^{242m}Am^{ƒ}  141–351 
No fission products 

^{241}Am^{ƒ}  ^{251}Cf^{ƒ}^{[11]}  430–900  
^{226}Ra^{№}  ^{247}Bk  1.3 k – 1.6 k  
^{240}Pu  ^{229}Th  ^{246}Cm^{ƒ}  ^{243}Am^{ƒ}  4.7 k – 7.4 k  
^{245}Cm^{ƒ}  ^{250}Cm  8.3 k – 8.5 k  
^{239}Pu^{ƒ}  24.1 k  
^{230}Th^{№}  ^{231}Pa^{№}  32 k – 76 k  
^{236}Np^{ƒ}  ^{233}U^{ƒ}  ^{234}U^{№}  150 k – 250 k  ‡  ^{99}Tc^{₡}  ^{126}Sn  
^{248}Cm  ^{242}Pu  327 k – 375 k  ^{79}Se^{₡}  
1.53 M  ^{93}Zr  
^{237}Np^{ƒ}  2.1 M – 6.5 M  ^{135}Cs^{₡}  ^{107}Pd  
^{236}U  ^{247}Cm^{ƒ}  15 M – 24 M  ^{129}I^{₡}  
^{244}Pu^{№}  80 M 
... nor beyond 15.7 M years^{[12]} 

^{232}Th^{№}  ^{238}U^{№}  ^{235}U^{ƒ№}  0.7 G – 14.1 G  
Legend for superscript symbols 
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 wellknown 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 "eveneven" isotopes are also less likely to undergo spontaneous fission, and they also have relatively much longer partial halflives for alpha or beta decay. Examples of these isotopes are uranium238 and thorium232. On the other hand, other than the lightest nuclides, nuclides with an odd number of protons and an odd number of neutrons (odd Z, odd N) are usually shortlived (a notable exception is neptunium236 with a halflife of 154,000 years) because they readily decay by betaparticle 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 halflife of such oddodd 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 halflife
 Be available in suitable quantities
Thermal neutrons^{[13]}  Epithermal neutrons  

σ_{F} (b)  σ_{γ} (b)  %  σ_{F} (b)  σ_{γ} (b)  %  
531  46  8.0%  ^{233}U  760  140  16% 
585  99  14.5%  ^{235}U  275  140  34% 
750  271  26.5%  ^{239}Pu  300  200  40% 
1010  361  26.3%  ^{241}Pu  570  160  22% 
Fissile nuclides in nuclear fuels include:
 Uranium235 which occurs in natural uranium and enriched uranium
 Plutonium239 bred from uranium238 by neutron capture

Plutonium241 bred from plutonium240 by neutron capture. The ^{240}
_{}Pu^{}
_{} comes from ^{239}
_{}Pu^{}
_{} by the same process.  Uranium233 bred from thorium232 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 mediumenergy 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 nonfissions are in the table at right.
See also
Notes
 ^ The fissile rule thus formulated indicates 33 isotopes as likely fissile: Th225, 227, 229; Pa228, 230, 232; U231, 233, 235; Np234, 236, 238; Pu237, 239, 241; Am240, 242, 244; Cm243, 245, 247; Bk246, 248, 250; Cf249, 251, 253; Es252, 254, 256; Fm255, 257, 259. Only fourteen (including a longlived metastable nuclear isomer) have halflives of at least a year: Th229, U233, U235, Np236, Pu239, Pu241, Am242m, Cm243, Cm245, Cm247, Bk248, Cf249, Cf251 and Es252. Of these, only U235 is naturally occurring. It is possible to breed U233 and Pu239 from more common naturally occurring isotopes (Th232 and U238 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 334335. [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.
 ^ "SlidesPart one: Kinetics". UNENE University Network of Excellence in Nuclear Engineering. Retrieved 3 January 2013.
 ^ James J. Duderstadt and Louis J. Hamilton (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0471223638.
 ^ John R. Lamarsh and Anthony John Baratta (Third Edition) (2001). Introduction to Nuclear Engineering. Prentice Hall. ISBN 0201824981.
 ^ Fissile Materials and Nuclear Weapons, International Panel on Fissile Materials
 ^ Plus radium (element 88). While actually a subactinide, it immediately precedes actinium (89) and follows a threeelement gap of instability after polonium (84) where no nuclides have halflives of at least four years (the longestlived nuclide in the gap is radon222 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.
 ^ Specifically from thermal neutron fission of U235, e.g. in a typical nuclear reactor.

^ Milsted, J.; Friedman, A. M.; Stevens, C. M. (1965). "The alpha halflife of berkelium247; a new longlived isomer of berkelium248". Nuclear Physics. 71 (2): 299. Bibcode:1965NucPh..71..299M. doi:10.1016/00295582(65)907194.
"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 Bk^{248} with a halflife greater than 9 y. No growth of Cf^{248} was detected, and a lower limit for the β^{−} halflife can be set at about 10^{4} y. No alpha activity attributable to the new isomer has been detected; the alpha halflife is probably greater than 300 y."  ^ This is the heaviest nuclide with a halflife of at least four years before the "Sea of Instability".
 ^ Excluding those "classically stable" nuclides with halflives significantly in excess of ^{232}Th; e.g., while ^{113m}Cd has a halflife of only fourteen years, that of ^{113}Cd is nearly eight quadrillion years.
 ^ "Interactive Chart of Nuclides". Brookhaven National Laboratory. Retrieved 20130812.