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# Spontaneous fission

Spontaneous fission (SF) is a form of radioactive decay characteristic of very heavy isotopes, and is theoretically possible for any atomic nucleus whose mass is greater than or equal to 100 u (elements near ruthenium). In practice, however, spontaneous fission is only energetically feasible for atomic masses above 230 u (elements near thorium). The elements most susceptible to spontaneous fission are the high-atomic-number actinide elements, such as mendelevium and lawrencium, and the trans-actinide elements, such as rutherfordium.

### Additional recommended knowledge

For uranium and thorium, the spontaneous fission mode of decay does occur, but is not seen for the majority of radioactive breakdowns and is usually neglected except for the exact considerations of branching ratios when determining the activity of a sample containing these elements. Mathematically, the criterion for whether spontaneous fission can occur is approximately:

$\hbox{Z}^2/\hbox{A}\ge45.$

Where Z is the atomic number and A is the mass number (e.g., 235 for U-235).

As the name suggests, spontaneous fission follows exactly the same process as nuclear fission, except that it occurs without the atom having been struck by a neutron or other particle. Spontaneous fissions release neutrons as all fissions do, so if a critical mass is present, a spontaneous fission can initiate a chain reaction. Also, radioisotopes for which spontaneous fission is a nonnegligible decay mode may be used as neutron sources; californium-252 (half-life 2.645 years, SF branch ratio 3.09%) is often used for this purpose. The neutrons may then be used to inspect airline luggage for hidden explosives, to gauge the moisture content of soil in the road construction and building industries, to measure the moisture of materials stored in silos, and in other applications.

As long as the fissions give a negligible reduction of the amount of nuclei that can spontaneously fission, this is a Poisson process: for very short time intervals the probability of a spontaneous fission is proportional to the length of time.

The spontaneous fission of uranium-238 leaves trails of damage in uranium containing minerals as the fission fragments recoil through the crystal structure. These trails, or fission tracks provide the basis for the radiometric dating technique: fission track dating.

## Spontaneous fission rates

Spontaneous fission rates:[1]

Nuclide Half-life Fission prob. per decay (%) Neutrons per fission Neutrons per (g.s)
U-235 7.04x108 years 2.0x10-7 % 1.86 3.0x10-4
U-238 4.47x109 years 5.4x10-5 % 2.07 0.0136
Pu-239 2.41x104 years 4.4x10-10 % 2.16 2.2x10-2
Pu-240 6,569 years 5.0x10-6 % 2.21 920
Cf-252 2.638 years 3.09 % 3.73 2.3x1012

In practice Pu-239 will invariably contain a certain amount of Pu-240 due to the tendency of Pu-239 to absorb an additional neutron during production. Pu-240's high rate of spontaneous fission events makes it an undesirable contaminant. Weapons-grade plutonium contains no more than 7% Pu-240.

The gun-type fission weapon has a critical insertion time of about 1ms, and the probability of a fission during this time interval should be small. Therefore only U-235 is suitable.

Spontaneous fission can occur much more rapidly when the nucleus of an atom undergoes Superdeformation.

## Notes

1. ^ Shultis, J. Kenneth; Richard E. Faw (2002). Fundamentals of Nuclear Science and Engineering. Marcel Dekker, Inc., pp. 137 (table 6.2). ISBN 0-8247-0834-2.