The Natural Nuclear Reactors At Oklo and Fundamental Constants

I'm sure I speak for all of us in the nuclear blogging community when I wish for Charles' complete recovery from his recent health problems. - NNadir



-"Untitled," Alberto Di Fabio, 2001, at the Nicolas Robinson Gallery, New York.

The following is a guest contribution to Nuclear Green by NNadir. It was originally published on DailyKos on February 19, 2012. Here is a link to the original, with an amusing poll: The Natural Nuclear Reactors At Oklo and Fundamental Constants



It appears that this will represent, should I publish it, the 373rd diary I've written at Daily Kos.

Um...um...jeeze...this after taking a break for a year or so...jeeze...

My first diary was in the last quarter of 2006, meaning that I've been at this for 5 and a half years, roughly, and the themes I've been at are pretty much constant, although I will confess that some of the research I've done in preparing my diaries has caused me to change my ideas about some things, but more or less the themes are constant.

Other things have remained more or less constant as well. No real progress has been made at slowing the rate of dangerous fossil fuel waste dumping into Earth's atmosphere - 5 years ago is roughly 150 billion tons of dumped dangerous fossil fuel waste - represented as carbon dioxide - ago, and roughly more than 10 million deaths from air pollution ago.

Time. Time moves on, no matter how you choose to measure it.

My fifth diary here was on the subject of the Oklo Natural Nuclear Reactors and recently - after hearing the same sort of constant things I hear about how the nuclear weapons waste in the Hanford tanks, near Richland, Washington, is going to kill everyone in Washington and Oregon, much as the Fukushima tsunami wiped out everyone in Japan because it hit nuclear reactors, and much as Chernobyl wiped out Kiev, Ukraine and much as Three Mile Island wiped out Harrisburg, PA - I was reminded about my long ago diary on Oklo.

My fifth diary got three comments, and three recommends. I should have quit while I was ahead.

The Oklo natural nuclear reactors operated almost 2 billion years ago, in an area of Africa that is now modern day Gabon, and physicists have been interested in them as they help calibrate the values of "fundamental constants" which may not, in fact, be "constant."


The start up of the Oklo reactors in a sandstone matrix almost certainly took place when oxygen - which was then a poison, since it wiped out 90% of the species on this planet, all of which were unicellular - appeared in the planetary atmosphere.

Most everybody knows - with the possible exception of members of Greenpeace since the overwhelming majority of them are blissfully unaware of the contents of science books - that natural uranium contains three isotopes, U-238, U-235, and U-234. Respectively these three isotopes have half lives of 4.468 billion years, 703.8 million years and 245,500 years. Since the earth is about 4.5 billion years old, the latter could not have survived from the primordial supernovae that account for all of the heavy elements found one earth, however it is in radioequilibrium with its parent nuclide, U-238, about half of which has survived since the formation of the earth. U-234 is formed by the following nuclear decay reactions:

U²³⁸ -> Th²³⁴ + He⁴

Th²³⁴ -> Pa²³⁴ + e^-

Pa²³⁴ -> U²³⁴ + e^-

The helium nucleus and the electrons in the above nuclear reactions - which have always taken place on earth - are travelling at very high speeds during these reactions and are respectively called alpha particles and beta particles, as everyone knows (unless, again, one is qualified to join Greenpeace). U²³⁴ is radioactive, much more radioactive than either of the other two uranium nuclei that naturally occur, but it is also at radioequilibrium, which is the condition obtained when a the radioactive isotope is decaying at almost precisely at the same rate as it is being formed. The isotope with the shortest half life is the one that is present in the smallest quantity, and despite the fact that U²³⁴ is highly radioactive when compared with U²³⁸, this is why the radioactivity of purified isolated uranium is trivial. If the parent nucleus is also radioactive (as is almost always the case) the ratio of the concentration of of the two isotopes present after equilibrium has been obtained is a function of their two half-lives.

The mathematics of this situation is relatively straightforward and a good description of it can be found at the website of the Nobel Prize winning organization - an anti-ignorance organization - the International Atomic Energy Agency, the IAEA.

Here's the link to the IAEA page on the laws of radioactive decay: Laws of Radioactive Decay.

As one can see therein, the relative concentration of two radioisotopes is given by the ratio of their decay constants, λ₁ and λ₂, wherein the value of λ_i is equal to the natural logarithm of 2 divided by t_1/2i, where t_1/2i is the half-life of the ith radioactive isotope. That is:

λ_i = ln(2)/ t_1/2i

The decay constant for U²³⁸ is 1.55 X 10^-10 years^-1 and for U²³⁴ is 2.82 X 10^-6 years^-1 and the ratio of these two constants is roughly 18,200. Thus for every atom of U²³⁴ in a sample of U²³⁸ at equilibrium, 18,200 atoms of the latter are present. Put another way, 0.0055% of uranium is the U²³⁴. This calculated result conforms almost exactly with the observed distribution of uranium isotopes in solid uranium ores. (The ocean is a dilute uranium ore, containing approximately 5 billion tons of uranium that has weathered out of rocks, however the ocean under certain conditions can be disturbed from reaching radioequilibrium owing to the low solubility of Th²³⁴, an intermediate short lived isotope between uranium isotopes, but the effect is extremely minor.)

So called "depleted uranium" is not at equilibrium. In the link above one can see that the time required to reach equilibrium between two radioactive isotopes is given by the relation:

t_max = (1/(λ₂-λ₁)) ln(λ₂ / λ₁)

For the U²³⁸, U²³⁴ couple, the period of time required for the isotopes to come to equilibrium is about 3.47 million years. This is much shorter than the age of the earth (unless of course you're Rick Santorum and think that the "biblical" age of the earth is incontrovertible) and thus all natural solid uranium is at equilibrium, but depleted uranium, which does not occur naturally (in most cases, excluding as we shall see, Oklo ores) cannot be more than 70 years old, is not.

So called "depleted" uranium is the least radioactive of all known types of uranium, since the same process that removes U²³⁵ from natural uranium also removes U²³⁴, at least in the case where gaseous diffusion - the most common process for uranium isotope separations - is used. (The much more modern but less widely employed laser excitation methods do not remove U²³⁴ quite as efficiently from natural uranium.)

Primordial U²³⁵ has survived since the accretion of the earth, since its half-life is long enough. If we take the age of the earth to be 4.5 billion years, roughly close to the half life of we can directly calculate that about 1.2% of the original U²³⁵ that was here when the earth formed is still here. Suppose we have a kilogram of natural uranium. This uranium would contain about 7 grams of U²³⁵, and 993 grams U²³⁸ along with trivial amounts of U²³⁴. The mass of uranium that is present survives from a larger mass that was present when the earth formed, roughly 1986 grams of original U²³⁸ and 589 grams of U²³⁵. Thus the concentration of the latter isotope would have been about 23% U-235 in the total uranium and the uranium would be far more enriched than the uranium in commercial nuclear reactors like those that have operated for 55 years or so. (Commercial reactors typically have enrichments between 2 and 5 percent.)

Uranium of this type could easily go critical under certain conditions, specifically in the presence of a moderator. About 2 billion years ago, all of the uranium found on earth was about 3.7% U-235, which is sufficiently concentrated to go critical in the presence of a water which is the main moderator used in commercial nuclear power plants. This is precisely what happened at Oklo.

As geologists know, many ores on earth are reduced ores. For instance the mineral sphalerite is zinc sulfide, ZnS. Pyrite is an ore of iron, and its formula is FeS₂, whereas mercury sulfide is the mineral cinnabar which has the formula HgS, and lead's ore is galena, PbS. The metals can be obtained from these ores by roasting them in air, during which the sulfur atoms (or in the case of pyrite, disulfide) are oxidized to sulfur oxides, which accounts for much of the air pollution involved with smelting operations. The formation of these ores takes place in reducing conditions in the absense of oxygen. Planets with atmospheric oxygen seem to be exceedingly rare in the universe, and earth was no exception to this general rule more than two billion years ago. However when photosynthesis evolved, the chemistry of the earth changed dramatically, owing to the growth in atmospheric oxygen, so that new ores that formed after the oxygen concentrations grew were often oxides.

In some cases, though obviously not all, ores of metals were converted from largely insoluble and immobile sulfides into oxygen species.

I mentioned that the earth's oceans contain billion ton quantities of uranium, which is actually only a fraction of the uranium that is present on the planet. (This uranium, along with radioactive thorium and radioactive potassium accounts for almost all of the internal heat of the earth.) Uranium oxides and oxo cations are slightly soluble in water, and thus can solvate. Moreover uranium has many well defined oxidation states and the mobilization of uranium is understood, even today - where it is widely studies because of the concern that uranium be "safe" for all eternity and injure no one, whereas no one can be safe, even for 15 seconds, from the effects of dangerous fossil fuel waste, a.k.a "air pollution - we understand that oxygen is responsible for the mobilization of uranium in either natural or synthetic (often unintended) uranium ores. Thus, happily, we understand the geochemistry of uranium extremely well. At Oklo, relatively diffuse concentrations of uranium oxides, which formed after other uranium species were exposed to oxygen either solvated in water or in the atmosphere, leached through porous sandstone where for chemical reasons they reprecipitated forming a common uranium ore known as pitchblende, which is largely UO₂ with some more oxidized material, UO₃ being present. The process went on for many millions of years, in the presence of water, which acted as a neutron moderator. Eventually the concentrations in these ores became so high that an appreciable flux of neutrons became present from spontaneous fission of uranium isotopes and their decay products and from the interaction of alpha particles with light elements to produce even more neutrons. Some of these neutrons caused nuclear fission. Probably for millions of years these fission events were what we now call "subcritical." Although stray neutrons from spontaneous fission in natural uranium - which, again, two billion years ago was "enriched" uranium - caused fission in other uranium atoms, more neutrons leaked out of the system or were absorbed in non-fissionable nuclei, than caused fissions. Eventually, as the deposits grew larger, the probability of neutrons leaking out of the ore bodies without striking a U²³⁵ atom became sufficiently small that a chain reaction started, in other words, the uranium ores went critical and a natural nuclear reactor started.

At Oklo, there were about 16 of these "reactor zones" or "RZ" as scientific papers sometimes call them.

They operated for about half a million years in a cyclic fashion, the cycles taking place because of a negative void coefficient, a feature of the vast majority of commercial reactors that now provide electricity to humanity. The power output of the reactors was small, roughly 100 kW(th). From the ratio of isotopes of the element lutetium - which is not appreciably a fission product, but which is nonetheless present in the reactor zones - scientists deduce that the operating temperature of the reactors was about 280^oC +/- 50^oC. This analysis is possible because the neutron capture cross section of the two natural isotopes of lutetium vary quite dramatically with temperature. (c.f. L.V. Krishnan "Oklo Natural Fission Reactor" Nuclear Energy Encyclopedia: Science, Technology, and Applications, First Edition (Wiley Series On Energy). Edited by Steven B. Krivit, Jay H. Lehr, and Thomas B. Kingery.© 2011 John Wiley & Sons, Inc. pp. 51-55.) These reactors were thermal reactors, meaning that they required a moderator, a substance with low atomic mass, to slow the neutrons down to speeds that are typical of molecules at what we now call "room temperature." As the reactors went critical, the water in them boiled and may have even vented as steam. The loss of this water deprived the reactors of a moderator, and thus the nuclear reaction stopped, only to restart when the reactors cooled and cool water diffused into them as groundwater.

The reactors operated, again, for half a million years, roughly on aveage, and their formation depended on a flux of water moving through them. What is interesting is to learn what happened to the fission products, most of which were radioactive in the beginning, that resulted from these reactors. The answer has been extensively analyzed in great detail, and the answer to the question is "not much." Over two billion years, most of the fission products in porous sandstone at Oklo didn't even migrate as far as Tom Brady can throw an errant football in a "Hail Mary" pass at the end of a Superbowl as a last ditch attempt to avoid a losing effort.

In two billion years.

Speaking of losing efforts, and losers, in order to prove that nuclear energy is as unsafe as dangerous fossil fuels, anti-nukes would need to establish that nuclear energy kills two million people per year, which is what air pollution, not counting climate change, kills every year. Despite much hopeful rhetoric on their part hoping that such a number of people would die from the destruction of three nuclear reactor cores at Fukushima after an earthquake and inundating tsunami, and lots of cheering for a hoped for disaster of this sort, even the destroyed reactors have not caused the death of anyone, never mind the two million people that die each year, every year, from the normal operations in which oil, gas, coal and biomass are burned in our threatened oxygen containing atmosphere. Thus far, despite much hoopla and wishful thinking, the Fukushima reactors in an earthquake and tsunami have not proved as dangerous as dams in an earthquake and tsunami, or buildings in an earthquake and tsunami, or cars in an earthquake and tsunami.

At Greenpeace they may be muttering "Wait 'til next year!" just like Tom Brady might be muttering the same thing for different reasons.

Anyway, to return to the point: The Oklo reactors were continuously inunated with water; their existance depended on the presence of water and oxygen, flowing water. There is no evidence that the unicellular life at that time made any effort to place the fission products in stabilized vitrified glass and steel containers, and of course, it seems that at no time in it's geological history over the past two billion years was Gabon a desert. It certainly isn't one now, although humanity is working on it.

So much for the theory that if Yucca Mountain had opened - and to be clear I opposed Yucca on the grounds that all of the constituents of used nuclear fuel are far too valuable to be dumped - that everyone in Nevada, Southern California, and Western Arizona would have died from radioactivity. I would guess that even if Nevada became a rain forest, that it would take millions of years for as many people to die from leached radioisotopes as will die in the next ten minutes from dumped dangerous fossil fuel waste from the normal operations of dangerous fossil fuel power plants and dangerous fossil fueled devices. That is I doubt that if opened, Yucca mountain would have been as dangerous as lawn mowers in New Jersey. As it happens, I live in New Jersey, and I assure you I am continuously breathing lawn mower dirt - especially the particulates that lawnmowers produce in the form of dangerous fossil fuel waste - in summers. Thus I am not "safe." The probability that I am immortal and will live forever is, um, zero. Lawn mower waste or even more likely something else, like say, my dietary habits, will kill me.

The fossil reactor cores at Oklo are somewhat depleted in the fission gas isotopes of xenon and krypton - the latter which would have in the case of the 85 isotope have long ago decayed into rubidium-85, Rb⁸⁵ making it the only non-radioactive rubidium on earth. (The other naturally occurring isotope of rubidium, Rb⁸⁷, is naturally radioactive, like potassium-40, K⁴⁰. ) Also depleted from the radioactive core is radiocesium. The half-lives of the radioactive isotopes of cesium are respectively for Cs¹³⁴, Cs^{135 Cs}136, Cs¹³⁷, are respectively, 2.05 years, 3 million years, 13 days, and 30.02 years. Cs¹³⁴ is not a fission product generally, the chief fission isotope at mass number 134 is an isotope of xenon, but is formed from the only stable, non-radioactive isotope of cesium, Cs¹³³, which is a fission product, by neutron capture. Cs¹³⁵ is often generated in relatively low concentrations because its (transient) parent nuclide, Xe¹³⁵ has one of the highest neutron capture cross sections known, resulting in its transformation into Xe¹³⁶, which was long regarded to be a stable nucleus, although modern physicists, because of a physics punctilio concerning the nuclear stability rules, were suspected that it was a very weakly radioactive nucleus. With very sensitive instrumentation, it is possible to detect radioactive decay in this "stable" isotope, Xe¹³⁶ and the apparent half-life appears to be on the order of 10²⁰ years.

Right here at DailyKos, after Fukushima I read a lot of stuff written by people about the ratios of cesium isotopes in the regions of the destroyed reactors. Like much else that was written about Fukushima here, particularly by the members of the superstition, fear and ignorance squad that calls itself "nuclear free DKos" it consisted mostly of scientific howlers. (Other howlers were written by that guy who says that nuclear energy has a "role to play" in the future, but it needs to be "safer," to which I respond, "safer than what?" There are no 10 exajoule scale per year forms of energy, not coal, not gas, not oil, and not dams that are as safe as nuclear energy. None. Zero.)

Cesium is, however, a mobile (and sometimes even volatile) fission product. Waste mentality type people have long considered how to dump cesium created in commercial nuclear reactors referring to it as "waste" - something I oppose because in the last several years I've come to understand this very precious element in new and exciting ways, especially the radioactive kind which could be used to solve major environmental problems that have nothing to do with nuclear power. My problem with radiocesium is not that there is too much of it, but that there is not enough of it. In any case an elegant solution for safely dumping cesium that would work very nicely - were it not a stupid thing to dump cesium - at all would be to make synthetic pollucite. Pollucite is one of the most stable minerals known. Some of the oldest rocks on earth, rocks in the Canadian shield that are close to 4 billion years old, contain pollucite. Essentially there are no other rocks that have survived as long on earth as those that contain pollucite.

One of the ironies about the 4 billion year old pollucite is that it is unlikely to survive humanity. Pollucite ores in Canada are already mined to obtain cesium, and the chief use of cesium today is to make lubricating agents for oil and gas drilling, including the infamous "fracking" schemes that all of our anti-nukes endorse, tacitly (sometimes via deliberate or static ignorance) or openly. By the way, all of the 4 billion year old pollucite is radioactive since pollucite contains both non-radioactive cesium and its cogener rubidium. All of the rubidium on earth - except for some obtained in an isotopically pure form created by letting radioactive krypton, Kr⁸⁵ decay into rubidium 85 that contains no Rb⁸⁷ - contains Rb⁸⁷ which is radioactive, but has a sufficiently long half life to have survived since the time at which the Earth formed.

Unicellular life forms that were present at the time that the Oklo reactors were operating seemed not to have thought of making synthetic pollucite to contain the radiocesium for all of eternity, and the cesium seems to have leached out of the Oklo fossil reactor cores. There is considerable evidence however that the process was very slow, and even incomplete. None of the radiocesium survived: It has all decayed to isotopes of barium. Because of the wide distribution of the half lives of radiocesium, we can measure the leach rates of cesium by looking at the distribution and distance from the cores of barium isotopes. The earliest leaching cesium would leave fossils of Ba¹³⁷ and Ba¹³⁴, whereas the last cesium to leave would leave the radiofossil Ba¹³⁵. Some work like this has been done, but it is incomplete thus far.

One reference for these types of studies is Geochimica et Cosmochimica Acta 72 (2008) 4123–4135, "Ba isotopic signature for early differentiation between Cs and Ba in natural fission reactors."

I very much doubt that if the cesium leached a long way - and maybe it didn't - that it would have been in a concentration that in modern times would be considered particularly hazardous. This is because any leaching would have taken a very long time, probably so long that all of the cesium-137 would have decayed to barium, leaving only the radioactive cesium-135 which has a relatively low specific activity and which necessarily would be further diluted by the very water flows that caused it to move in the first place. It may not have even been comparable to in radiological concentrations to the radioactive potassium at that time, since the half-life of K⁴⁰ is 1.227 billion years, meaning that two billion years ago, potassium was, by appeal to the radioactive decay laws, 3.1 times as radioactive as it is today.

Some years back I noted in this space that as a result of nuclear weapons testing, as well as Chernobyl, that Cs-137 is now widely distributed on earth. Every Cloud Has A Silver Lining, Even Mushroom Clouds: Cs-137 and Watching the Soil Die. We know a lot from modern experience how cesium behaves in the geosphere and atmosphere and it moves surprisingly slowly in many types of systems.

It is a matter of some irony that since the wide distribution of Cs¹³⁷, mostly in the 1940s, 1950s and 1960s, that worldwide human life expectancy has increased dramatically. This of course is most likely not because of such distribution and is probably in spite of such distribution, although the increase in life expectancy obviously places some restrictions on the magnitude of the planetary toxicology of Cs¹³⁷.



Today many places where radiocesium is leaching underground are known, most famously in the United States, from the Hanford "waste" tanks, mentioned at the opening of this diary, where the by products of the extraction of plutonium for nuclear weapons was dumped for several decades without much consideration for their composition. There are also known comparable sites in the former Soviet Union and elsewhere. These migrations are being exhaustively monitored, and many thousands of papers on the migration of cesium in the geosphere/atmosphere/hydrosphere/biosphere have been written and I have personally read lots of them. They're very interesting things to read when you have nothing else to do during a bout of insomnia.

In any case it is clear that the majority of stuff that leached out of the pitchblende uranium ores that went critical about 2 billion years ago was cesium. Nothing else went all that far, not even, surprisingly, the pertechnate ion.

I've gone on a quite a length about the nature of the fission products at Oklo and one of these that I haven't mentioned, Sm¹⁴⁹ has been studied extensively by theoretical physicists in connection with ascertaining whether important physical constants, the fundamental constants are, as described in the title and opening paragraphs of this diary, are in fact, constant.

What are the "fundamental constants?"

They are a set of "constants" that are required for the standard model of physics which seeks to integrate the electromagnetic, weak nuclear force and the strong nuclear force. They can be abstract, but in some cases, they show up in every day life. The following quotation is taken from a recent paper Nuclear Physics B (Proc. Suppl.) 203–204 (2010) 3–17 entitled "The fundamental constants in physics and their possible time variation."

The 28 fundamental constants, which appear in the basic laws of physics, are not understood, but they are important parameters, relevant for all fields of physics, e.g. particle physics, astrophysics, cosmology, nuclear physics, solid state physics, atomic physics or laser physics. But they are also relevant for chemistry or biology. In chemistry and biology only the seven constants, relevant for the stable matter in the universe, play a role. These are Newtons gravity constant G, the fine structure constant, the mass of the electron, the QCD scale parameter and they masses of the light quarks u, d and s. In particle physics many more parameters enter, which are related to weak decays or to unstable particles – in total one has 28 fundamental parameters.

The rest of this admittedly too long diary will address the fine structure constant, usually designated a α. I made a somewhat sarcastic reference to this constant in an earlier diary in this space, Oh. Oh. Plutonium Contamination Suspected. In any case it is this constant, α whose drift has been evaluated by appeal to the operations of the Oklo natural nuclear reactors.

That the fundemental constants might drift was originally a speculation of the great Swiss/English/American physicist Paul Dirac who posited a law that can be stated this way:

Any two of the very large dimensionless numbers occurring in Nature are
connected by a simple mathematical relation, in which the coefficients are
of the order of magnitude unity.

(cf. Prog. Theor. Phys. 126 (2011), 993-1019) This speculation lead to a further speculation that the fundamental constants might not be constant and a great many scientists have searched the universe, literally, as much of spacetime that is accessible to human vision, to confirm or deny this possibility, which is potentially of huge theoretical portent.

A physicist named Shlyakhter proposed that the drift of the fine structure constant should be discernable by examining the amount of an isotope of Samarium, Sm¹⁴⁹ present in the fossil reactors. Over the years, many considerations of the neutronics of these reactors have been undertaken is a spectacular multidisplinary undertaking in which geologists, nuclear chemists, nuclear engineers, theoretical physicists and geochemists have participated.

A seminal paper was written by Freeman Dyson, of the Institute of Advanced Study (he was recruited by Robert Oppenheimer to take the job) one of the most important physicists never to have been awarded the Nobel Prize - Nobel Laureate Steven Weinberg has described the Nobel Committee as having "fleeced" Dyson by not awarding Dyson the prize - Dyson showed how the distribution of samarium at Oklo was related to the historic (2 billion years ago) value of the fine structure constant, via an appeal to the Breit-Wigner formulation for neutron capture resonances.

Here is a interview with Freeman Dyson discussing Samarium-149 and the Oklo reactors

Dyson, who is now approaching 90 is something of a strange bird: Despite more than 50 years at the Institute of Advanced Study - which was of course, the last institution at which Albert Einstein worked, and is today is the home institution of people like Andrew Wiles - Dyson never actually bothered to get a Ph.D. but became an important physicist anyway. Dyson did much in the physics community to point out the importance to physics of Richard Feynman's work on quantum electrodynamics, an area in which Dyson did much work himself. By using a passive, unemotional voice, he convinced the American military establishment to not use nuclear weapons in Vietnam by claiming that it would be bad strategically. Indeed.

For much of his career on the side he was one of the dying breed - common in the middle of the twentieth century - of techno-utopians who pushed for space flight to Mars and Saturn using nuclear explosions to propel ships and proposed designing genetic material for species that could survive on the surface of comets.

Dyson, with the nuclear engineering pioneer Alvin Weinberg - who has almost saintly status among modern advocates of nuclear energy - was a pioneer in the theory of global climate change even though he has become a bête noire among modern climate activists for his contention that even if climate change is real - this is his claim and certainly not mine -it's not so bad and ought to be more or less ignored, maybe even encouraged. (For these reason he and James Hansen have exchanged some rather nasty insults for one another.) A liberal Democrat, Dyson was an enthusiastic supporter of Barack Obama, but was dismissive of Al Gore...

Here's a New York Times Magazine Profile of Freeman Dyson and some of the controversy surrounding him.

Irrespective of these controversies, Dyson showed that the fine structure constant could not have varied by more than -0.9 X 10^-7 and 1.2 X 10^-7 over the last 2 billion years, adding to his list of prodigious intellectual achievements.

The Oklo reactors have generated a lot of interest for a lot of reasons in a number of disiplines. Besides showing the behavior of fission products on billion year time scales, they offer real insight to the history of the universe as a whole, as well as the history of the earth.

The reactors were discovered, by the way, when French uranium mining engineers discovered that the uranium at Oklo would prove pretty much useless for nuclear power plants of their time (this was in the early 1970's), owing to the depletion of U²³⁵ in the ores, which had fissioned in nuclear reactors two billion years before. While this may have proved a disappointment to the mining officials, it has proved to be a boon to scientific understanding.

Interesting I think.

Have a nice evening.