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 (e.g., iron-56); spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at greater atomic mass numbers.[1]

History

By 1908, physicists understood that alpha decay involved ejection of helium nuclei from a decaying atom.[2] Like cluster decay, alpha decay is not typically categorized as a process of fission.[3]

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[4][5] by their observations of uranium in the Moscow Metro Dinamo station, 60 metres (200 ft) underground.[6]

Feasibility

Elemental

Spontaneous fission occurs over practical observation times only in nuclides with a mass number of at least 232; these are nuclei 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 number 100 onward.

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, or in applications that are very sensitive to even minuscule numbers of fission neutrons (such as nuclear weapon design).

Mathematical

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

{\hbox{Z}}^{2}/{\hbox{A}}\approx 47.

where Z is the atomic number and A is the mass number (e.g., $Z 2 / A = 36$ for uranium-235). However, no known radioactive isotope except oganesson-294 reaches a value of 47 (approximately 47.36), and 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 Z²/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[7]
Nuclide	Half-life (yrs)	Fission rate (% of decays)	Neutrons per		Spontaneous half-life (yrs)	Z²/A
Nuclide	Half-life (yrs)	Fission rate (% of decays)	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[8]	~74	3.31	01.6·10¹⁰	1.12·10⁴	36.9
²⁵² Cf	02.6468[9]	3.09	3.73	02.3·10¹²	85.7	38.1

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

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 ²³⁵U is suitable. Almost all nuclear bombs use some kind of implosion method.

Spontaneous fission can occur much faster when a nucleus 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 tunnelling, 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 3.1%) 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 fission is directly proportional to the length of time.

The spontaneous fission of uranium-238 and uranium-235 leaves 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

Sadhukhan, Jhilam (29 October 2020). "Microscopic Theory for Spontaneous Fission". Frontiers in Physics. 8: 567171. Bibcode:2020FrP.....8..418S. doi:10.3389/fphy.2020.567171.
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. Bibcode:2009JPhG...36a5107S. doi:10.1088/0954-3899/36/1/015107.
Scharff-Goldhaber, G.; Klaiber, G. S. (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". Nato.int. Retrieved 7 July 2022.
Petrzhak, Konstantin. "How the spontaneous fission was discovered" (in Russian).
Shultis, J. Kenneth; Faw, Richard E. (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

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[1] Sadhukhan, Jhilam (29 October 2020). "Microscopic Theory for Spontaneous Fission". Frontiers in Physics. 8: 567171. Bibcode:2020FrP.....8..418S. doi:10.3389/fphy.2020.567171.

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

[3] 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. Bibcode:2009JPhG...36a5107S. doi:10.1088/0954-3899/36/1/015107.

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

[5] "Igor Sutyagin: The role of nuclear weapons and its possible future missions". Nato.int. Retrieved 7 July 2022.

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

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

[8] Entry at periodictable.com

[9] Entry at periodictable.com