Natural nuclear fission reactor

Last updated June 07, 2024

A natural nuclear fission reactor is a uranium deposit where self-sustaining nuclear chain reactions occur. The conditions under which a natural nuclear reactor could exist were predicted in 1956 by Paul Kuroda.^[1] The remnants of an extinct or fossil nuclear fission reactor, where self-sustaining nuclear reactions have occurred in the past, are verified by analysis of isotope ratios of uranium and of the fission products (and the stable daughter nuclides of those fission products). This was first discovered in 1972 in Oklo, Gabon by researchers from French Commissariat à l'énergie atomique (CEA) under conditions very similar to Kuroda's predictions.

Oklo is the only location where this phenomenon is known to have occurred, and consists of 16 sites with patches of centimeter-sized ore layers. There, self-sustaining nuclear fission reactions are thought to have taken place approximately 1.7 billion years ago, during the Statherian period of the Paleoproterozoic, and continued for a few hundred thousand years, probably averaging less than 100 kW of thermal power during that time.^[2]^[3]^[4] During that era, life on Earth consisted of little more than aquatic single-cell organisms.

The "Oklo phenomenon" was discovered in June 1972 by the laboratory at the uranium enrichment plant in Pierrelatte, France. Routine analysis of a sample of natural uranium revealed a slight but abnormal deficit of uranium 235 (²³⁵U)⁶. The normal proportion of ²³⁵U is 0.7202%, whereas this sample showed only 0.7171%.

Discovery of the Oklo fossil reactors

In May 1972 at the Tricastin uranium enrichment site at Pierrelatte in France, routine mass spectrometry comparing UF₆ samples from the Oklo mine showed a discrepancy in the amount of the ²³⁵
U isotope. Normally the concentration is 0.72% while these samples had only 0.60%, a significant difference (some 17% less U-235 was contained in the samples than expected).^[5] This discrepancy required explanation, as all civilian uranium handling facilities must meticulously account for all fissionable isotopes to ensure that none are diverted to the construction of nuclear weapons. Furthermore, since fissile material is why people mine uranium, a significant amount "going missing" was also of direct economic concern.

Thus the French Commissariat à l'énergie atomique (CEA) began an investigation. A series of measurements of the relative abundances of the two most significant isotopes of uranium mined at Oklo showed anomalous results compared to those obtained for uranium from other mines. Further investigations into this uranium deposit discovered uranium ore with a ²³⁵
U concentration as low as 0.44% (almost 40% below the normal value). Subsequent examination of isotopes of fission products such as neodymium and ruthenium also showed anomalies, as described in more detail below. However, the trace radioisotope ²³⁴
U did not deviate significantly in its concentration from other natural samples. Both depleted uranium and reprocessed uranium will usually have ²³⁴
U concentrations significantly different from the secular equilibrium of 55 ppm ²³⁴
U relative to ²³⁸
U. This is due to ²³⁴
U being enriched together with ²³⁵
U and due to it being both consumed by neutron capture and produced from ²³⁵
U by fast neutron induced (n,2n) reactions in nuclear reactors. In Oklo any possible deviation of ²³⁴
U concentration present at the time the reactor was active would have long since decayed away. ²³⁶
U must have also been present in higher than usual ratios during the time the reactor was operating, but due to its half life of 2.348×10⁷ years being almost two orders of magnitude shorter than the time elapsed since the reactor operated, it has decayed to roughly 1.4×10⁻²² its original value and thus basically nothing and below any abilities of current equipment to detect.

This loss in ²³⁵
U is exactly what happens in a nuclear reactor. A possible explanation was that the uranium ore had operated as a natural fission reactor in the distant geological past. Other observations led to the same conclusion, and on 25 September 1972 the CEA announced their finding that self-sustaining nuclear chain reactions had occurred on Earth about 2 billion years ago. Later, other natural nuclear fission reactors were discovered in the region.^[4]


Nd	143	144	145	146	148	150
C/M	0.99	1.00	1.00	1.01	0.98	1.06

Fission product isotope signatures

Neodymium

The neodymium found at Oklo has a different isotopic composition to that of natural neodymium: the latter contains 27% ¹⁴²
Nd, while that of Oklo contains less than 6%. The ¹⁴²
Nd is not produced by fission; the ore contains both fission-produced and natural neodymium. From this ¹⁴²
Nd content, we can subtract the natural neodymium and gain access to the isotopic composition of neodymium produced by the fission of ²³⁵
U. The two isotopes ¹⁴³
Nd and ¹⁴⁵
Nd lead to the formation of ¹⁴⁴
Nd and ¹⁴⁶
Nd by neutron capture, and this excess must be corrected (see above) to obtain perfect agreement between this corrected isotopic composition and that deduced from fission yields.

Ruthenium

Similar investigations into the isotopic ratios of ruthenium at Oklo found a much higher ⁹⁹
Ru concentration than otherwise naturally occurring (27–30% vs. 12.7%). This anomaly could be explained by the decay of ⁹⁹
Tc to ⁹⁹
Ru. In the bar chart the normal natural isotope signature of ruthenium is compared with that for fission product ruthenium which is the result of the fission of ²³⁵
U with thermal neutrons. It is clear that the fission ruthenium has a different isotope signature. The level of ¹⁰⁰
Ru in the fission product mixture is low because fission produces neutron rich isotopes which subsequently beta decay and ¹⁰⁰
Ru would only be produced in appreciable quantities by double beta decay of the very long-lived (half life 7.1×10¹⁸ years) molybdenum isotope ¹⁰⁰
Mo. On the timescale of when the reactors were in operation, very little (about 0.17 ppb) decay to ¹⁰⁰
Ru will have occurred. Other pathways of ¹⁰⁰
Ru production like neutron capture in ⁹⁹
Ru or ⁹⁹
Tc (quickly followed by beta decay) can only have occurred during high neutron flux and thus ceased when the fission chain reaction stopped.

Mechanism

The natural nuclear reactor at Oklo formed when a uranium-rich mineral deposit became inundated with groundwater, which could act as a moderator for the neutrons produced by nuclear fission. A chain reaction took place, producing heat that caused the groundwater to boil away; without a moderator that could slow the neutrons, however, the reaction slowed or stopped. The reactor thus had a negative void coefficient of reactivity, something employed as a safety mechanism in human-made light water reactors. After cooling of the mineral deposit, the water returned, and the reaction restarted, completing a full cycle every 3 hours. The fission reaction cycles continued for hundreds of thousands of years and ended when the ever-decreasing fissile materials, coupled with the build-up of neutron poisons, no longer could sustain a chain reaction.

Fission of uranium normally produces five known isotopes of the fission-product gas xenon; all five have been found trapped in the remnants of the natural reactor, in varying concentrations. The concentrations of xenon isotopes, found trapped in mineral formations 2 billion years later, make it possible to calculate the specific time intervals of reactor operation: approximately 30 minutes of criticality followed by 2 hours and 30 minutes of cooling down (exponentially decreasing residual decay heat) to complete a 3-hour cycle.^[6] Xenon-135 is the strongest known neutron poison. However, it is not produced directly in appreciable amounts but rather as a decay product of Iodine-135 (or one of its parent nuclides). Xenon-135 itself is unstable and decays to caesium-135 if not allowed to absorb neutrons. While caesium-135 is relatively long lived, all caesium-135 produced by the Oklo reactor has since decayed further to stable barium-135. Meanwhile, Xenon-136, the product of neutron capture in xenon-135 only decays extremely slowly via double beta decay and thus scientists were able to determine the neutronics of this reactor by calculations based on those isotope ratios almost two billion years after it stopped fissioning uranium.

A key factor that made the reaction possible was that, at the time the reactor went critical 1.7 billion years ago, the fissile isotope ²³⁵
U made up about 3.1% of the natural uranium, which is comparable to the amount used in some of today's reactors. (The remaining 96.9% was non-fissile ²³⁸
U and roughly 55 ppm ²³⁴
U.) Because ²³⁵
U has a shorter half-life than ²³⁸
U, and thus decays more rapidly, the current abundance of ²³⁵
U in natural uranium is only 0.72%. A natural nuclear reactor is therefore no longer possible on Earth without heavy water or graphite.^[7]

The Oklo uranium ore deposits are the only known sites in which natural nuclear reactors existed. Other rich uranium ore bodies would also have had sufficient uranium to support nuclear reactions at that time, but the combination of uranium, water, and physical conditions needed to support the chain reaction was unique, as far as is currently known, to the Oklo ore bodies. It is also possible that other natural nuclear fission reactors were once operating but have since been geologically disturbed so much as to be unrecognizable, possibly even "diluting" the uranium so far that the isotope ratio would no longer serve as a "fingerprint". Only a small part of the continental crust and no part of the oceanic crust reaches the age of the deposits at Oklo or an age during which isotope ratios of natural uranium would have allowed a self sustaining chain reaction with water as a moderator.

Another factor which probably contributed to the start of the Oklo natural nuclear reactor at 2 billion years, rather than earlier, was the increasing oxygen content in the Earth's atmosphere.^[4] Uranium is naturally present in the rocks of the earth, and the abundance of fissile ²³⁵
U was at least 3% or higher at all times prior to reactor startup. Uranium is soluble in water only in the presence of oxygen.^{[ citation needed ]} Therefore, increasing oxygen levels during the aging of the Earth may have allowed uranium to be dissolved and transported with groundwater to places where a high enough concentration could accumulate to form rich uranium ore bodies. Without the new aerobic environment available on Earth at the time, these concentrations probably could not have taken place.

It is estimated that nuclear reactions in the uranium in centimeter- to meter-sized veins consumed about five tons of ²³⁵
U and elevated temperatures to a few hundred degrees Celsius.^[4]^[8] Most of the non-volatile fission products and actinides have only moved centimeters in the veins during the last 2 billion years.^[4] Studies have suggested this as a useful natural analogue for nuclear waste disposal.^[9] The overall mass defect from the fission of five tons of ²³⁵
U is about 4.6 kilograms (10 lb). Over its lifetime the reactor produced roughly 100 megatonnes of TNT (420 PJ) in thermal energy, including neutrinos. If one ignores fission of plutonium (which makes up roughly a third of fission events over the course of normal burnup in modern human-made light water reactors), then fission product yields amount to roughly 129 kilograms (284 lb) of technetium-99 (since decayed to ruthenium-99), 108 kilograms (238 lb) of zirconium-93 (since decayed to niobium-93), 198 kilograms (437 lb) of caesium-135 (since decayed to barium-135, but the real value is probably lower as its parent nuclide, xenon-135, is a strong neutron poison and will have absorbed neutrons before decaying to ¹³⁵
Cs in some cases), 28 kilograms (62 lb) of palladium-107 (since decayed to silver), 86 kilograms (190 lb) of strontium-90 (long since decayed to zirconium), and 185 kilograms (408 lb) of caesium-137 (long since decayed to barium).

Relation to the atomic fine-structure constant

The natural reactor of Oklo has been used to check if the atomic fine-structure constant α might have changed over the past 2 billion years. That is because α influences the rate of various nuclear reactions. For example, ¹⁴⁹
Sm captures a neutron to become ¹⁵⁰
Sm, and since the rate of neutron capture depends on the value of α, the ratio of the two samarium isotopes in samples from Oklo can be used to calculate the value of α from 2 billion years ago.

Several studies have analysed the relative concentrations of radioactive isotopes left behind at Oklo, and most have concluded that nuclear reactions then were much the same as they are today, which implies that α was the same too.^[10]^[11]^[12]

Related Research Articles

Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.

In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series or "positive feedback loop" of these reactions. The specific nuclear reaction may be the fission of heavy isotopes. A nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

<span class="mw-page-title-main">Nuclear reactor</span>

A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nuclear fission is passed to a working fluid, which in turn runs through steam turbines. These either drive a ship's propellers or turn electrical generators' shafts. Nuclear generated steam in principle can be used for industrial process heat or for district heating. Some reactors are used to produce isotopes for medical and industrial use, or for production of weapons-grade plutonium. As of 2022, the International Atomic Energy Agency reports there are 422 nuclear power reactors and 223 nuclear research reactors in operation around the world.

<span class="mw-page-title-main">Uranium</span> Chemical element, symbol U and atomic number 92

Uranium is a chemical element; it has symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Uranium radioactively decays, usually by emitting an alpha particle. The half-life of this decay varies between 159,200 and 4.5 billion years for different isotopes, making them useful for dating the age of the Earth. The most common isotopes in natural uranium are uranium-238 and uranium-235. Uranium has the highest atomic weight of the primordially occurring elements. Its density is about 70% higher than that of lead and slightly lower than that of gold or tungsten. It occurs naturally in low concentrations of a few parts per million in soil, rock and water, and is commercially extracted from uranium-bearing minerals such as uraninite.

In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal chain reaction can only be achieved with fissile material. The predominant neutron energy in a system may be typified by either slow neutrons or fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives.

The nuclear fuel cycle, also called nuclear fuel chain, is the progression of nuclear fuel through a series of differing stages. It consists of steps in the front end, which are the preparation of the fuel, steps in the service period in which the fuel is used during reactor operation, and steps in the back end, which are necessary to safely manage, contain, and either reprocess or dispose of spent nuclear fuel. If spent fuel is not reprocessed, the fuel cycle is referred to as an open fuel cycle ; if the spent fuel is reprocessed, it is referred to as a closed fuel cycle.

<span class="mw-page-title-main">Uranium-238</span> Isotope of uranium

Uranium-238 is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, it is fissionable by fast neutrons, and is fertile, meaning it can be transmuted to fissile plutonium-239. ²³⁸U cannot support a chain reaction because inelastic scattering reduces neutron energy below the range where fast fission of one or more next-generation nuclei is probable. Doppler broadening of ²³⁸U's neutron absorption resonances, increasing absorption as fuel temperature increases, is also an essential negative feedback mechanism for reactor control.

<span class="mw-page-title-main">Nuclear fission product</span> Atoms or particles produced by nuclear fission

Nuclear fission products are the atomic fragments left after a large atomic nucleus undergoes nuclear fission. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons, the release of heat energy, and gamma rays. The two smaller nuclei are the fission products..

<span class="mw-page-title-main">Uranium-234</span> Isotope of uranium

Uranium-234 is an isotope of uranium. In natural uranium and in uranium ore, ²³⁴U occurs as an indirect decay product of uranium-238, but it makes up only 0.0055% of the raw uranium because its half-life of just 245,500 years is only about 1/18,000 as long as that of ²³⁸U. Thus the ratio of ²³⁴
U to ²³⁸
U in a natural sample is equivalent to the ratio of their half-lives. The primary path of production of ²³⁴U via nuclear decay is as follows: uranium-238 nuclei emit an alpha particle to become thorium-234. Next, with a short half-life, ²³⁴Th nuclei emit a beta particle to become protactinium-234 (²³⁴Pa), or more likely a nuclear isomer denoted ^234mPa. Finally, ²³⁴Pa or ^234mPa nuclei emit another beta particle to become ²³⁴U nuclei.

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The thorium fuel cycle is a nuclear fuel cycle that uses an isotope of thorium, ²³²
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U which is the nuclear fuel. Unlike natural uranium, natural thorium contains only trace amounts of fissile material, which are insufficient to initiate a nuclear chain reaction. Additional fissile material or another neutron source is necessary to initiate the fuel cycle. In a thorium-fuelled reactor, ²³²
Th absorbs neutrons to produce ²³³
U. This parallels the process in uranium breeder reactors whereby fertile ²³⁸
U absorbs neutrons to form fissile ²³⁹
Pu. Depending on the design of the reactor and fuel cycle, the generated ²³³
U either fissions in situ or is chemically separated from the used nuclear fuel and formed into new nuclear fuel.

<span class="mw-page-title-main">Spent nuclear fuel</span> Nuclear fuel thats been irradiated in a nuclear reactor

Spent nuclear fuel, occasionally called used nuclear fuel, is nuclear fuel that has been irradiated in a nuclear reactor. It is no longer useful in sustaining a nuclear reaction in an ordinary thermal reactor and, depending on its point along the nuclear fuel cycle, it will have different isotopic constituents than when it started.

<span class="mw-page-title-main">Fission products (by element)</span> Breakdown of nuclear fission results

This page discusses each of the main elements in the mixture of fission products produced by nuclear fission of the common nuclear fuels uranium and plutonium. The isotopes are listed by element, in order by atomic number.

Xenon-135 (¹³⁵Xe) is an unstable isotope of xenon with a half-life of about 9.2 hours. ¹³⁵Xe is a fission product of uranium and it is the most powerful known neutron-absorbing nuclear poison, with a significant effect on nuclear reactor operation. The ultimate yield of xenon-135 from fission is 6.3%, though most of this is from fission-produced tellurium-135 and iodine-135.

Uranium-236 (²³⁶U) is an isotope of uranium that is neither fissile with thermal neutrons, nor very good fertile material, but is generally considered a nuisance and long-lived radioactive waste. It is found in spent nuclear fuel and in the reprocessed uranium made from spent nuclear fuel.

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<span class="mw-page-title-main">Liquid fluoride thorium reactor</span> Type of nuclear reactor that uses molten material as fuel

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Nuclear transmutation is the conversion of one chemical element or an isotope into another chemical element. Nuclear transmutation occurs in any process where the number of protons or neutrons in the nucleus of an atom is changed.

References

↑ Kuroda, P. K. (1956). "On the Nuclear Physical Stability of the Uranium Minerals". Journal of Chemical Physics. 25 (4): 781–782, 1295–1296. Bibcode:1956JChPh..25..781K. doi:10.1063/1.1743058.
↑ Meshik, A. P. (November 2005). "The Workings of an Ancient Nuclear Reactor". Scientific American. 293 (5): 82–6, 88, 90–1. Bibcode:2005SciAm.293e..82M. doi:10.1038/scientificamerican1105-82. PMID 16318030.
↑ Mervin, Evelyn (July 13, 2011). "Nature's Nuclear Reactors: The 2-Billion-Year-Old Natural Fission Reactors in Gabon, Western Africa". blogs.scientificamerican.com. Retrieved July 7, 2017.
1 2 3 4 5 Gauthier-Lafaye, F.; Holliger, P.; Blanc, P.-L. (1996). "Natural fission reactors in the Franceville Basin, Gabon: a review of the conditions and results of a "critical event" in a geologic system". Geochimica et Cosmochimica Acta. 60 (23): 4831–4852. Bibcode:1996GeCoA..60.4831G. doi:10.1016/S0016-7037(96)00245-1.
↑ Davis, E. D.; Gould, C. R.; Sharapov, E. I. (2014). "Oklo reactors and implications for nuclear science". International Journal of Modern Physics E. 23 (4): 1430007–236. arXiv: 1404.4948 . Bibcode:2014IJMPE..2330007D. doi:10.1142/S0218301314300070. ISSN 0218-3013. S2CID 118394767.
↑ Meshik, A. P.; et al. (2004). "Record of Cycling Operation of the Natural Nuclear Reactor in the Oklo/Okelobondo Area in Gabon". Physical Review Letters . 93 (18): 182302. Bibcode:2004PhRvL..93r2302M. doi:10.1103/PhysRevLett.93.182302. PMID 15525157.
↑ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 1257. ISBN 978-0-08-037941-8.
↑ De Laeter, J. R.; Rosman, K. J. R.; Smith, C. L. (1980). "The Oklo Natural Reactor: Cumulative Fission Yields and Retentivity of the Symmetric Mass Region Fission Products". Earth and Planetary Science Letters. 50 (1): 238–246. Bibcode:1980E&PSL..50..238D. doi:10.1016/0012-821X(80)90135-1.
↑ Gauthier-Lafaye, F. (2002). "2 billion year old natural analogs for nuclear waste disposal: the natural nuclear fission reactors in Gabon (Africa)". Comptes Rendus Physique. 3 (7–8): 839–849. Bibcode:2002CRPhy...3..839G. doi:10.1016/S1631-0705(02)01351-8.
↑ New Scientist: Oklo Reactor and fine-structure value. June 30, 2004.
↑ Petrov, Yu. V.; Nazarov, A. I.; Onegin, M. S.; Sakhnovsky, E. G. (2006). "Natural nuclear reactor at Oklo and variation of fundamental constants: Computation of neutronics of a fresh core". Physical Review C. 74 (6): 064610. arXiv: hep-ph/0506186 . Bibcode:2006PhRvC..74f4610P. doi:10.1103/PHYSREVC.74.064610. S2CID 118272311.
↑ Davis, Edward D.; Hamdan, Leila (2015). "Reappraisal of the limit on the variation in α implied by the Oklo natural fission reactors". Physical Review C. 92 (1): 014319. arXiv: 1503.06011 . Bibcode:2015PhRvC..92a4319D. doi:10.1103/physrevc.92.014319. S2CID 119227720.

Sources

Bentridi, S.E.; Gall, B.; Gauthier-Lafaye, F.; Seghour, A.; Medjadi, D. (2011). "Génèse et évolution des réacteurs naturels d'Oklo" [Inception and evolution of Oklo natural nuclear reactors]. Comptes Rendus Geoscience (in French). 343 (11–12): 738–748. Bibcode:2011CRGeo.343..738B. doi:10.1016/j.crte.2011.09.008.

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[1] Kuroda, P. K. (1956). "On the Nuclear Physical Stability of the Uranium Minerals". Journal of Chemical Physics. 25 (4): 781–782, 1295–1296. Bibcode:1956JChPh..25..781K. doi:10.1063/1.1743058.

[2] Meshik, A. P. (November 2005). "The Workings of an Ancient Nuclear Reactor". Scientific American. 293 (5): 82–6, 88, 90–1. Bibcode:2005SciAm.293e..82M. doi:10.1038/scientificamerican1105-82. PMID 16318030.

[3] Mervin, Evelyn (July 13, 2011). "Nature's Nuclear Reactors: The 2-Billion-Year-Old Natural Fission Reactors in Gabon, Western Africa". blogs.scientificamerican.com. Retrieved July 7, 2017.

[Gauthier-Lafaye1996-4] 1 2 3 4 5 Gauthier-Lafaye, F.; Holliger, P.; Blanc, P.-L. (1996). "Natural fission reactors in the Franceville Basin, Gabon: a review of the conditions and results of a "critical event" in a geologic system". Geochimica et Cosmochimica Acta. 60 (23): 4831–4852. Bibcode:1996GeCoA..60.4831G. doi:10.1016/S0016-7037(96)00245-1.

[DavisGould2014-5] Davis, E. D.; Gould, C. R.; Sharapov, E. I. (2014). "Oklo reactors and implications for nuclear science". International Journal of Modern Physics E. 23 (4): 1430007–236. arXiv: 1404.4948 . Bibcode:2014IJMPE..2330007D. doi:10.1142/S0218301314300070. ISSN 0218-3013. S2CID 118394767.

[6] Meshik, A. P.; et al. (2004). "Record of Cycling Operation of the Natural Nuclear Reactor in the Oklo/Okelobondo Area in Gabon". Physical Review Letters . 93 (18): 182302. Bibcode:2004PhRvL..93r2302M. doi:10.1103/PhysRevLett.93.182302. PMID 15525157.

[Greenwood1257-7] Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 1257. ISBN 978-0-08-037941-8.

[8] De Laeter, J. R.; Rosman, K. J. R.; Smith, C. L. (1980). "The Oklo Natural Reactor: Cumulative Fission Yields and Retentivity of the Symmetric Mass Region Fission Products". Earth and Planetary Science Letters. 50 (1): 238–246. Bibcode:1980E&PSL..50..238D. doi:10.1016/0012-821X(80)90135-1.

[9] Gauthier-Lafaye, F. (2002). "2 billion year old natural analogs for nuclear waste disposal: the natural nuclear fission reactors in Gabon (Africa)". Comptes Rendus Physique. 3 (7–8): 839–849. Bibcode:2002CRPhy...3..839G. doi:10.1016/S1631-0705(02)01351-8.

[10] New Scientist: Oklo Reactor and fine-structure value. June 30, 2004.

[11] Petrov, Yu. V.; Nazarov, A. I.; Onegin, M. S.; Sakhnovsky, E. G. (2006). "Natural nuclear reactor at Oklo and variation of fundamental constants: Computation of neutronics of a fresh core". Physical Review C. 74 (6): 064610. arXiv: hep-ph/0506186 . Bibcode:2006PhRvC..74f4610P. doi:10.1103/PHYSREVC.74.064610. S2CID 118272311.

[12] Davis, Edward D.; Hamdan, Leila (2015). "Reappraisal of the limit on the variation in α implied by the Oklo natural fission reactors". Physical Review C. 92 (1): 014319. arXiv: 1503.06011 . Bibcode:2015PhRvC..92a4319D. doi:10.1103/physrevc.92.014319. S2CID 119227720.

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