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.

History

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]

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. 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.

Mathematical

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

{\frac {Z^{2}}{A}}\geq 47.

^[7]

where Z is the atomic number and A is the mass number (e.g., $Z 2 / A = 36$ 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

Spontaneous fission rates^[8]
Nu- clide	Half-life (yrs)	Fission prob. per decay (%)	Neutrons per		Spontaneous half-life (yrs)	⁠Z²/A⁠
Nu- clide	Half-life (yrs)	Fission prob. per decay (%)	Fission	Gram-sec	Spontaneous half-life (yrs)	⁠Z²/A⁠
²³⁵ U	7.04·10⁸	2.0·10⁻⁷	1.86	000.0003	3.5·10¹⁷	36.0
²³⁸ U	4.47·10⁹	5.4·10⁻⁵	2.07	000.0136	8.4·10¹⁵	35.6
²³⁹ Pu	24100	4.4·10⁻¹⁰	2.16	000.022	5.5·10¹⁵	37.0
²⁴⁰ Pu	06569	5.0·10⁻⁶	2.21	920	1.16·10¹¹	36.8
²⁵⁰ Cm	08300 ^[9]	~74	3.31	01.6·10¹⁰	1.12·10⁴	36.9
²⁵² Cf	02.6468^[10]	3.09	3.73	02.3·10¹²	85.7	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.

Notes

^ Rutherford, E.; Royds, T. (1908). "XXIV.Spectrum of the radium emanation". Philosophical Magazine. series 6. 16 (92): 313–317. doi:10.1080/14786440808636511.
^ Santhosh, K P; Biju, R K (1 January 2009). "Alpha decay, cluster decay and spontaneous fission in (294–326)122 isotopes". Journal of Physics G: Nuclear and Particle Physics. 36 (1): 015107. doi:10.1088/0954-3899/36/1/015107.
^ G. Scharff-Goldhaber and G. S. Klaiber (1946). "Spontaneous Emission of Neutrons from Uranium". Phys. Rev. 70 (3–4): 229. Bibcode:1946PhRv...70..229S. doi:10.1103/PhysRev.70.229.2.
^ Igor Sutyagin: The role of nuclear weapons and its possible future missions
^ Petrzhak, Konstantin. "How the spontaneous fission was discovered" (in Russian).
^ Dorin N Poenaru; et al. (1984). "Spontaneous emission of heavy clusters". Journal of Physics G: Nuclear Physics. 10 (8): L183–L189. Bibcode:1984JPhG...10L.183P. doi:10.1088/0305-4616/10/8/004.
^ Krane, Kenneth S. (1988). Introductory Nuclear Physics. John Wiley & Sons. pp. 483–484 (Equation 13.3). ISBN 978-0-471-80553-3.
^ Shultis, J. Kenneth; Richard E. Faw (2008). Fundamentals of Nuclear Science and Engineering. CRC Press. pp. 141 (table 6.2). ISBN 978-1-4200-5135-3.
^ Entry at periodictable.com
^ Entry at periodictable.com

External links

The LIVEChart of Nuclides - IAEA with filter on spontaneous fission decay

[1] Rutherford, E.; Royds, T. (1908). "XXIV.Spectrum of the radium emanation". Philosophical Magazine. series 6. 16 (92): 313–317. doi:10.1080/14786440808636511.

[2] Santhosh, K P; Biju, R K (1 January 2009). "Alpha decay, cluster decay and spontaneous fission in (294–326)122 isotopes". Journal of Physics G: Nuclear and Particle Physics. 36 (1): 015107. doi:10.1088/0954-3899/36/1/015107.

[3] G. Scharff-Goldhaber and G. S. Klaiber (1946). "Spontaneous Emission of Neutrons from Uranium". Phys. Rev. 70 (3–4): 229. Bibcode:1946PhRv...70..229S. doi:10.1103/PhysRev.70.229.2.

[4] Igor Sutyagin: The role of nuclear weapons and its possible future missions

[5] Petrzhak, Konstantin. "How the spontaneous fission was discovered" (in Russian).

[6] Dorin N Poenaru; et al. (1984). "Spontaneous emission of heavy clusters". Journal of Physics G: Nuclear Physics. 10 (8): L183–L189. Bibcode:1984JPhG...10L.183P. doi:10.1088/0305-4616/10/8/004.

[7] Krane, Kenneth S. (1988). Introductory Nuclear Physics. John Wiley & Sons. pp. 483–484 (Equation 13.3). ISBN 978-0-471-80553-3.

[8] Shultis, J. Kenneth; Richard E. Faw (2008). Fundamentals of Nuclear Science and Engineering. CRC Press. pp. 141 (table 6.2). ISBN 978-1-4200-5135-3.

[9] Entry at periodictable.com

[10] Entry at periodictable.com

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