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{{Nuclear physics}}

'''Spontaneous fission''' (SF) is a form of [[radioactive decay]] that is found only in very heavy [[chemical element]]s. The [[nuclear binding energy]] of the elements reaches its maximum at an [[atomic mass number]] of about 56; spontaneous breakdown into smaller nuclei and a few isolated [[nuclear particle]]s becomes possible at greater atomic mass numbers.

== History ==
The first [[nuclear fission]] process discovered was fission induced by [[neutron]]s. Because [[cosmic ray]]s produce some neutrons, it was difficult to distinguish between induced and spontaneous events. Cosmic rays can be reliably shielded by a thick layer of rock or water. Spontaneous fission was identified in 1940 by [[Soviet Union|Soviet]] physicists [[Georgy Flyorov]] and [[Konstantin Petrzhak]]<ref>{{cite journal |author=G. Scharff-Goldhaber and G. S. Klaiber |year=1946 |title=Spontaneous Emission of Neutrons from Uranium |journal=Phys. Rev. |volume=70 |issue=3–4 |pages=229  |doi=10.1103/PhysRev.70.229.2|bibcode = 1946PhRv...70..229S }}</ref><ref>[http://www.nato.int/acad/fellow/94-96/sutyagin/01-02.htm Igor Sutyagin: The role of nuclear weapons and its possible future missions]</ref> by their observations of uranium in the [[Moscow Metro]] [[Dinamo (Moscow Metro)|Dinamo]] station, {{convert|60|m}} underground.<ref>{{cite web |url=http://n-t.ru/ri/ps/pb092.htm |first=Konstantin |last=Petrzhak |authorlink=Konstantin Petrzhak |title=How the spontaneous fission was discovered |lang=ru }}</ref>

[[Cluster decay]] was shown to be a superasymmetric spontaneous fission process.<ref>{{cite journal |author= Dorin N Poenaru|year=1984 |title=Spontaneous emission of heavy clusters|journal=Journal of Physics G: Nuclear Physics|volume=10 |issue=8 |pages=L183–L189|doi=10.1088/0305-4616/10/8/004|bibcode = 1984JPhG...10L.183P |display-authors=etal|author-link=Dorin N Poenaru }}</ref>

== Feasibility ==
=== Elemental ===

Spontaneous fission is feasible over practical observation times only for atomic masses of 232 amu or more. These are elements at least as heavy as [[thorium-232]] – which has a [[half-life]] somewhat longer than the age of the [[universe]]. <sup>232</sup>Th, <sup>235</sup>U, and <sup>238</sup>U are [[primordial nuclide]]s and have left evidence of undergoing spontaneous fission in their minerals.

The known elements most susceptible to spontaneous fission are the synthetic high-atomic-number [[actinide elements|actinides]] and [[transactinide]]s with atomic numbers from 100 onwards.

For naturally occurring thorium-232, [[uranium-235]], and [[uranium-238]], spontaneous fission does occur rarely, but in the vast majority of the radioactive decay of these atoms, [[alpha decay]] or [[beta decay]] occurs instead. Hence, the spontaneous fission of these isotopes is usually negligible, except in using the exact branching ratios when finding the [[radioactivity]] of a sample of these elements.

=== Mathematical ===
The [[liquid drop model]] predicts approximately that spontaneous fission can occur in a time short enough to be observed by present methods when
: <math>\frac{Z^2}{A} \ge 47.</math><ref>{{cite book |last=Krane |first=Kenneth S. |title=Introductory Nuclear Physics |publisher=[[John Wiley & Sons]] |year=1988 |pages=483–484 (Equation 13.3) |isbn=978-0-471-80553-3 }}</ref>

where ''Z'' is the [[atomic number]] and A is the [[mass number]] (e.g., {{math|''Z''{{sup|2}}/''A'' {{=}} 36}} for uranium-235). However, all known nuclides which undergo spontaneous fission as their main decay mode do not reach this value of 47, as the liquid drop model is not very accurate for the heaviest known nuclei due to strong shell effects.

== Spontaneous fission rates ==
[[File:(SF) Halflife of Radionulides depending on Z² to A ratio.png|thumb|upright=1.9|floatright|Spontaneous fission half-life of various nuclides depending on their ''Z''{{sup|2}}/''A'' ratio. Nuclides of the same element are linked with a red line. The green line shows the upper limit of half-life. Data taken from [[:fr:Fission spontanée#Noyaux décroissant par fission spontanée|French Wikipedia]].]]
{| class="wikitable"
|+ Spontaneous fission rates<ref>{{cite book 
  | last = Shultis
  | first = J. Kenneth
  | author2=Richard E. Faw
  | title = Fundamentals of Nuclear Science and Engineering
  | publisher = [[CRC Press]]
  | year = 2008
  | pages = 141 (table 6.2)
  | isbn = 978-1-4200-5135-3
 | title-link = Fundamentals of Nuclear Science and Engineering
 }}</ref>
|-
! rowspan="2" | Nu-<br>clide
! rowspan="2" | Half-life<br>(yrs)
! rowspan="2" | Fission {{abbr|prob.|probability}}<br>per decay (%)
! colspan="2" | Neutrons per
! rowspan="2" | Spontaneous<br>half-life (yrs)
! rowspan="2" | {{sfrac|''Z''<sup>2</sup>|''A''}}
|-
! Fission
! Gram-sec
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Uranium|235}}
| 7.04·10<sup>8</sup>
| 2.0·10<sup>−7</sup>
| 1.86
| {{0}}{{0}}0.0003
| 3.5·10<sup>17</sup>
| 36.0
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Uranium|238}}
| 4.47·10<sup>9</sup>
| 5.4·10<sup>−5</sup>
| 2.07
| {{0}}{{0}}0.0136
| 8.4·10<sup>15</sup> 
| 35.6
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Plutonium|239}}
| 24100
| 4.4·10<sup>−10</sup>
| 2.16
| {{0}}{{0}}0.022
| 5.5·10<sup>15</sup> 
| 37.0
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Plutonium|240}}
| {{0}}6569 
| 5.0·10<sup>−6</sup>
| 2.21
| 920
| 1.16·10<sup>11</sup> 
| 36.8
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Curium|250}}
| {{0}}8300&nbsp;<ref>[http://www.periodictable.com/Isotopes/096.250/index.dm.html Entry at periodictable.com]</ref>
| {{abbr|~|Approximately}}74
| 3.31
| {{0}}1.6·10<sup>10</sup>
| 1.12·10<sup>4</sup>
| 36.9
|-
| style="text-align:center;" | {{SimpleNuclide2|link=yes|Californium|252}}
| {{0}}2.6468<ref>[http://www.periodictable.com/Isotopes/098.252/index.dm.html Entry at periodictable.com]</ref>
| 3.09
| 3.73
| {{0}}2.3·10<sup>12</sup>
| 85.7
| 38.1
|}

In practice, {{SimpleNuclide2|Plutonium|239}} will invariably contain a certain amount of {{SimpleNuclide2|Plutonium|240}} due to the tendency of {{SimpleNuclide2|Plutonium|239}} to absorb an additional neutron during production. {{SimpleNuclide2|Plutonium|240}}'s high rate of spontaneous fission events makes it an undesirable contaminant. Weapons-grade plutonium contains no more than 7.0% {{SimpleNuclide2|Plutonium|240}}.

The rarely used [[gun-type fission weapon|gun-type atomic bomb]] has a [[insertion time|critical insertion time]] of about one millisecond, and the probability of a fission during this time interval should be small. 
Therefore, only {{SimpleNuclide2|Uranium|235}} is suitable. Almost all nuclear bombs use some kind of [[Nuclear weapon design#Implosion-type weapon|implosion method]].

Spontaneous fission can occur much more rapidly when the nucleus of an atom undergoes [[superdeformation]].

== Poisson process ==
Spontaneous fission gives much the same result as induced [[nuclear fission]]. However, like other forms of radioactive decay, it occurs due to [[quantum tunneling]], without the atom having been struck by a neutron or other particle as in induced nuclear fission. Spontaneous fissions release neutrons as all fissions do, so if a critical mass is present, a spontaneous fission can initiate a self-sustaining chain reaction. Radioisotopes for which spontaneous fission is not negligible can be used as neutron sources. For example, [[californium]]-252 (half-life 2.645 years, SF branch ratio about 3.1 [[percent]]) can be used for this purpose. The neutrons released can be used to inspect airline luggage for hidden explosives, to gauge the moisture content of soil in [[highway]] and building construction, or to measure the moisture of materials stored in silos, for example.

As long as the spontaneous fission gives a negligible reduction of the number of nuclei that can undergo such fission, this process can be approximated closely as a [[Poisson process]]. In this situation, for short time intervals the probability of a spontaneous fission is [[directly proportional]] to the length of time.

The spontaneous fission of uranium-238 and uranium-235 does leave trails of damage in the [[crystal structure]] of uranium-containing minerals when the fission fragments recoil through them. These trails, or ''fission tracks'', are the foundation of the [[radiometric dating]] method called [[fission track dating]].

== See also ==

* [[Natural nuclear fission reactor]]

== Notes ==
{{reflist}}

== External links==
* [[File:Ndslivechart.png]] '''[http://www-nds.iaea.org/livechart The LIVEChart of Nuclides - IAEA ]''' with filter on spontaneous fission decay
{{Nuclear_processes}}

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