Spontaneous fission

Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. 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 particles becomes possible at greater atomic mass numbers.


By 1908, the process of alpha decay was known to consist of the ejection of helium nuclei from the decaying atom;[1] however, as with cluster decay, alpha decay is not typically categorized as a process of fission.[2]

The first nuclear fission process discovered was fission induced by neutrons. Because cosmic rays 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 physicists Georgy Flyorov and Konstantin Petrzhak[3][4] by their observations of uranium in the Moscow Metro Dinamo station, 60 metres (200 ft) underground.[5]

Cluster decay was shown to be a superasymmetric spontaneous fission process.[6]



Spontaneous fission is feasible over practical observation times only for atomic masses of 232 atomic mass units or more. These are elements at least as heavy as thorium-232 鈥 which has a half-life somewhat longer than the age of the universe. 232Th, 235U, and 238U are primordial nuclides 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 actinides and transactinides 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.


The liquid drop model predicts approximately that spontaneous fission can occur in a time short enough to be observed by present methods when


where Z is the atomic number and A is the mass number (e.g., Z2/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

Spontaneous fission half-life of various nuclides depending on their Z 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 French Wikipedia.
Spontaneous fission rates [8]
Fission prob.
per decay (%)
Neutrons per Spontaneous
half-life (yrs)
Fission Gram-sec
7.04路108 2.0路10鈭7 1.86 000.0003 3.5路1017 36.0
4.47路109 5.4路10鈭5 2.07 000.0136 8.4路1015 35.6
24100 4.4路10鈭10 2.16 000.022 5.5路1015 37.0
06569 5.0路10鈭6 2.21 920 1.16路1011 36.8
08300 [9] ~74 3.31 01.6路1010 1.12路104 36.9
02.6468[10] 3.09 3.73 02.3路1012 85.7 38.1

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

The rarely used gun-type atomic bomb has a critical insertion time of about one millisecond, and the probability of a fission during this time interval should be small. Therefore, only 235
is suitable. Almost all nuclear bombs use some kind of 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