# 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 58; spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at greater atomic mass numbers.

Because of constraints in forming the daughter fission-product nuclei, spontaneous fission into known nuclides becomes theoretically possible (that is, energetically possible) for some atomic nuclei with atomic masses greater than 92 atomic mass units (amu), with the probability of spontaneous fission increasing as the atomic mass increases above this value.

## History

The first nuclear fission process discovered was the 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[1][2] by their observations of uranium in the Moscow Metro Dinamo station, 60 metres (200 ft) underground.[3]

Cluster decay was shown to be a superasymmetric spontaneous fission process.[4]

## Feasibility

### Elemental

Chart of nuclides (isotopes) depicting the valley of stability by type of decay. The diagonal line corresponds to equal numbers of neutrons and protons. Black squares are stable nuclides. Elements with more than 20 protons must have an increasing number of neutrons than protons to be stable. Nuclides with excessive neutrons or protons are unstable and prone to β (teal) or β+ (pink) decay, respectively. Spontaneous fission decays (SF, green) occur only for nuclides in the far upper right, that is nuclides with high atomic and neutron numbers.

The lightest natural nuclides that are hypothetically subject to spontaneous fission are niobium-93 and molybdenum-94 (elements 41 and 42, respectively)[verification needed]. Spontaneous fission has never been observed in the naturally occurring isotopes of these elements, however. In practice, these are stable isotopes.

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. Thorium-232 is the lightest primordial nuclide that has left evidence of undergoing spontaneous fission in its 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, 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

Within the framework of liquid drop model, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately:

${\displaystyle {\hbox{Z}}^{2}/{\hbox{A}}\geq 47.}$[5]

where Z is the atomic number and A is the mass number (e.g. ${\displaystyle {\hbox{Z}}^{2}/{\hbox{A}}}$ = 36 for uranium-235).

## Spontaneous fission rates

Spontaneous fission rates:[6]

Nuclide Half-life Fission prob. per decay Neutrons per fission Neutrons per gram-second Spontaneous half life Z2/A
235
U
7.04×108 years 2.0×10−9 1.86 3.0×10−4 3.5×1017 years 36.0
238
U
4.47×109 years 5.4×10−7 2.07 0.0136 8.4×1015 years 35.6
239
Pu
2.41×104 years 4.4×10−12 2.16 0.022 5.5×1015 years 37.0
240
Pu
6569 years 5.0×10−8 2.21 920 1.16×1011 years 36.8
250
Cm
6900 years 0.61 3.31 1.6×1010 N/A 36.9
252
Cf
2.638 years 3.09×10−2 3.73 2.3×1012 N/A 38.1

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

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
U
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.