‘A Precambrian physicist would have found it almost easy to build a nuclear reactor.’
George A. Cowan1
‘“What do I see landing in the fields nearby but a German plane … Two men get out, very polite, and ask me the way to Switzerland … one of them comes over to me holding something like a rock in his hand … and says, “This is for your trouble; take good care of it, it's uranium.” You understand it was the end of the war, … they no longer had the time to make the atomic bomb and they didn't need uranium anymore.”
“Of course I believe you”, I responded heroically. “But was it really uranium?”
“Absolutely: anyone could have seen that. It had an incredible weight, and when you touched it, it was hot. Besides, I still have it at home. I keep it on the terrace in a little shed, a secret, so the kids can't touch it; every so often I show it to my friends, and it's remained hot, it's hot even now.”'
Primo Levi, Uranium
On 2 June 1972 Dr Bouzigues made a worrying discovery,3 the sort of discovery that could have untold political, scientific or even criminal implications. Bouzigues worked on the staff at the Pierrelatte nuclear fuel reprocessing plant in France. One of his routine tasks was to measure the composition of ores coming from uranium mines near the river Oklo in the former French colony now known as the West African Republic of Gabon, about 440 kilometres from the Atlantic coast, shown in Figure 11.1. Time after time he checked the fraction of the natural ore that was in the form of the uranium-235 isotope compared to that in the form of the uranium-238 isotope by conducting analyses of uranium hexafluoride gas samples.4 The difference between the two isotopes is crucial. Naturally occurring uranium that we mine out of the Earth is almost all in the form of the 238 isotope.5 This form of uranium will not create a chain of self-sustaining nuclear reactions. If it did, our planet would have exploded a long time ago. In order to make a bomb or a productive chain reaction it is necessary to have traces of the active 235 isotope of uranium. In natural uranium no more than a fraction of a per cent is in the 235 form, whereas about 20 per cent is required for a chain of nuclear reactions to be initiated. Weapons-grade or ‘enriched’ uranium actually contains 90 per cent of the 235 isotope. These numbers allow us to sleep soundly at night secure in the knowledge that the Earth beneath us will not spontaneously begin an unstoppable chain of nuclear reactions that turn the Earth into a gigantic bomb. But who knows, maybe somewhere there is more 235 than average?
Bouzigues measured the 235 to 238 isotope ratios with great accuracy. They were important checks on the quality of materials that would ultimately be used in the French nuclear industry. This was routine work but on that June day in 1972 his attention to detail was rewarded. He noticed that some samples displayed a 235 to 238 ratio of 0.717 per cent instead of the usual value of 0.720 per cent usually found in all terrestrial samples – and even in meteorites and Moon rocks. So accurately was the ‘usual’ value known from experience6 and so precisely was it reflected in all the samples taken that this small discrepancy sounded alarm bells. Where was the missing 0.003 per cent of uranium-235? It was as if the uranium had already been used to fuel a nuclear reactor and so the 235 abundance had been depleted before it was mined out.
Figure 11.1 The location of Oklo in West Africa.
All sorts of possibilities were considered by the French Atomic Energy Commission. Perhaps the samples had been contaminated by some used fuel from the processing plant? But there was no evidence of any of the intense radioactivity that would accompany spent fuel, and no depleted uranium hexafluoride was missing from the plant's inventory. Some form of terrorist theft of material or extraterrestrial deposit was even suggested. But gradually the investigations found the source of the discrepancy to lie in the natural uranium deposits themselves. There was a naturally low 235 to 238 ratio in the mine site seams. The investigators looked at each step of the uranium ore's transportation and processing, from the original ore mining and local milling in Gabon, to the processing in France before it reached the enrichment plant at Pierrelatte. Nothing untoward was discovered. The uranium from the Oklo mine was just different from that found anywhere else. Indeed, samples that had been kept from all the shipments dispatched to France since the mine began excavating in 1970 all showed slight uranium-235 depletion. Out of the 700 tons of uranium already mined, the total ‘missing’ mass of uranium-235 amounted to 200 kilograms.
As the mine site was investigated in greater and greater detail it was soon clear that the missing uranium-235 had been destroyed within the mine seams. One possibility is that some chemical reactions had removed it whilst leaving the 238 unscathed. Unfortunately, the relative abundances of uranium-235 and 238 are not affected differently by chemical processes that have occurred inside the Earth. Such processes can make some parts of the Earth rich in uranium ore at the expense of others by dissolving it and moving it around, but they don't alter the balance of the two isotopes that make up the dissolved or suspended ore. Only nuclear reactions and decays can do that (see Figure 11.2).
Gradually, the unexpected truth dawned on the investigators. The depleted seams of uranium-235 contained the distinctive pattern of 30 or more other atomic elements that are formed as by-products of nuclear fission reactions. Their abundances were completely unlike those occurring naturally in the rocks where fission reactions had not occurred. The tell-tale signature of nuclear fission products is known from man-made reactor experiments. Six of these distinctive seams of natural nuclear reactor activity were eventually identified at Oklo. Some of the elements present, like neodymium, have many isotopes but not all are fission products. The non-fission products therefore provide a gauge of the abundance of all the isotopes before the natural reactions began and so enable us to determine the effects and running-times of those reactions.7
Figure 11.2 The fission of a uranium-235 nucleus.
Remarkably, it appeared that Nature had conspired to produce a natural nuclear reactor which had produced spontaneous nuclear reactions below the Earth's surface two billion years ago.8 It was this episode in the geological history of Gabon that had led to the accumulation of fission products at the site of the present-day mine. As a result of these sensational discoveries, mining was stopped for a period in 1972 while a detailed geochemical survey was carried out. Eventually, 15 fossilised ancient reactor sites were found, 14 of them at Oklo and another about 35 km to the south, at Bangombe.
In 1956, a Japanese physicist named Paul Kuroda, working at Arkansas University, had predicted that just such a thing might happen in Nature.9 Kuroda considered almost all of the key requirements: the concentrations of uranium needed for nuclear reactions, the time in the past when it might happen and the uranium-235 to 238 ratio.10 But nowhere could he think of a site on Earth where all these special conditions could be met at once. But Kuroda missed one interesting possibility that the Oklo geology had created for itself.
The first man-made nuclear reactions were produced on 2 December 1942 as part of the famous Manhattan Project that culminated in the creation of the first atomic bombs. They broke heavy nuclei into lighter ones, releasing energy and fast-moving neutrons which went on to break up more heavy nuclei and release yet more energy and neutrons. Man-made reactors are controlled by introducing a ‘moderator’, like graphite or water, which absorbs neutrons and slows the reaction. Neutrons are emitted with high speeds and in that state are readily absorbed by uranium-238 nuclei. They need to be slowed down considerably in order to have a high probability of being absorbed by another uranium-235 nucleus and so sustain the chain of fission reactions. Rods of graphite can be introduced into the interaction region and retracted when needed to moderate the reactions. Without this moderating effect nuclear reactions would snowball out of control once they have reached a critical level. So what moderated events at Oklo?
Investigators found the distinctive ‘smoking gun’ of fission products at Oklo, showing that nuclear chain reactions had taken place. Although today the natural abundance of uranium-235 is only about 0.7 per cent relative to uranium-238, the ratio of the two isotopes has not been constant throughout the history of the Earth. They both decay slowly but at different rates. The half-life of 235 is about 700 million years while that of 238 is about 4.5 billion years. The faster decay of 235 means that there was more 235 relative to 238 in the past than there is today. When the Earth formed about 4.5 billion years ago, natural uranium contained about 17 per cent uranium-235. After about 2.5 billion years, when the Earth was 2 billion years old, the 235:238 ratio would have fallen to around 3 per cent, just about right to start a chain reaction that could be moderated by water.
The Oklo uranium deposits were first discovered in the 1960s and are several kilometres long and about 700 metres wide. They derive from uranium originally deposited in the Earth's crust during the formation of the Earth. The original abundance was quite small, on average just a few parts in a million of the Earth's make-up. Its source, like all the other heavy elements in the Earth, lies in the stars. Uranium was formed in the stars and ejected into space before condensing into small rocks that were aggregated into solid planets during the early history of the solar system. Following the intense geological activity associated with the era after the formation of the Earth, the Oklo natural reactors were made possible by the accidental deposition of a uranium-rich seam inside a layer of sandstone lying on top of sheets of granite. Over millions of years nearly a kilometre of sandy sediment was washed down on top of the uranium. The granite layers are tilted at about 45 degrees and this led to a build up of rainwater and soluble uranium oxide deep underground at the bottom of the slope (see Figure 11.3).
The oxidising environment needed to create the water required to concentrate the uranium was brought about by a significant change in the Earth's biosphere. About two billion years ago a change of atmosphere occurred, brought about by the growth of blue-green algae, the first organisms able to carry out photosynthesis. Their activity increased the oxygen content of the water and allowed some of the uranium to change into soluble oxides. At Oklo, the uranium deposits were buried deep enough to prevent them being redissolved and dispersed during nearly two billion years of subsequent history. Only during the last two million years have parts of the ore deposit come close to the surface where it was found by mineral prospectors and mined out.
This is not the end of the special circumstances needed for a natural reactor. The layer of concentrated uranium ore needs to be thick enough to prevent the neutrons created by the first nuclear reactions from simply escaping and it must also be free from contamination by neutron poisons that will absorb all the neutrons and shut down the chain reactions.
Figure 11.3 The geology of the Oklo reactor site features granite layers tilted at about 45 degrees. This created a build-up of rainwater and soluble uranium oxide deep underground.
Once the soluble uranium reached a concentration of more than about 10 per cent two billion years ago, nuclear reactions could not only commence but continue in a stable self-regulated fashion. The seams needed to be at least half a metre thick in order that the neutrons did not just escape and the reactions die out. As the reactions went faster, so the temperature increased, turning the water into steam and slowing the neutrons that collided with the water molecules. This slowdown reduced the temperature, causing the steam to condense back into liquid water and reducing the number of neutrons absorbed. As a result the reactions then speeded up. This cycle of stop-go activity seems to have been repeated intermittently over nearly a million years, with episodes of chain reaction lasting for periods varying from just a few years to thousands of years before the reactor finally switched itself off .11 At six sites within the Oklo uranium layer about a ton of uranium235 had fissioned away,12 producing a million times more energy than would have been produced by the long-winded process of natural radioactive decay into uranium-238. At each site, the characteristic pattern of fission decay products remains to tell the tale.13 This is remarkable enough, but the insights that followed have made the Oklo reactors an important touchstone for our understanding of the constants of Nature.
‘To my mind radio-activity is a real disease of matter. Moreover it is a contagious disease. It spreads. You bring those debased and crumbling atoms near others and those too presently catch the trick of swinging themselves out of coherent existence. It is in matter exactly what the decay of our old culture is in society, a loss of traditions and distinctions and assured reactions.’
H.G. Wells, Tono-Bungay14
Alexander Shlyakhter was a remarkable young nuclear physicist from St Petersburg (Figure 11.4). He died of cancer in June 2000 after moving to Harvard University in the United States. His expertise was important in the control and understanding of several nuclear accidents, notably the disaster at the Chernobyl reactor in the former Soviet Union. Whilst still a student he realised that the remnants of the past Oklo nuclear activity might be telling us something very important about how nuclear reactions operated two billion years ago. He recognised that there was something very unusual about some of the nuclear reactions involved at Oklo. Remarkably, one of the reactions that occurred there, the capture of a neutron by a samarium149 nucleus to produce the samarium-150 isotope and a photon of light, is very sensitive. It only occurs because of a fortuitous ‘resonance’: the dramatic increase in the rate of a nuclear reaction in a particular narrow energy range. This occurrence of a resonance is rather like a hole-in-one in golf. It happens when the energies of the incoming components of a reaction have energies which add up to give a total that is almost exactly equal to the energy state of a possible outcome. In that case the interaction goes through very swiftly into its nicely located final state. It was just the same type of coincidence that Fred Hoyle had predicted should occur in the carbon nucleus which we described in Chapter 8.
Shlyakhter realised that the need for a very precisely located resonant energy level for the capture of a neutron by samarium-149 meant that the Oklo reactor was telling us something very remarkable about the constancy of physics over billions of years. The very finely tuned coincidences that appear to exist between the values of the different constants of Nature which determine the precise energy of this resonance level must have been in place to high accuracy about two billion years ago when the natural reactor was running. In Figure 11.5 we show the probability for the samarium reaction to occur at different temperatures if we shift the present position of the resonance energy. A zero shift means it has the same value as observed in nuclear reactions today.
The resonant character of neutron capture by samarium-149 is responsible for its very significant depletion at the Oklo site. Three of the four forces of Nature, the strong nuclear interaction, the weak interaction and the electromagnetic interaction, play a role in setting the location of the crucial resonance energy level. Unfortunately, the way in which they do so cannot be calculated in full detail because of the sheer complexity of the competing contributions. But Shlyakhter cut through these complexities by making the reasonable estimate that the contribution of each force of Nature to the resonance energy level would be in proportion to its strength. By assuming the temperature of the reactor was about 300 degrees centigrade – the boiling point ofthe water in the high-pressure environment of the seam – he concluded that 2 billion years ago the resonance level could not have been more than 20 milli electron volts (meV) away from its present position: that is a change of less than one part in 5 billion over 2 billion years.
Figure 11.4 Alexander Shlyakhter (1951–2000).15
These deductions mean that if the interaction strength between a single neutron and the samarium nucleus is changing then its rate of change is16 less than 10–19 per year, or less than about one part in abillion over the 14-billion year history of the Universe. Shlyakhter argued17 that if the interaction strength is determined predominantly by the strong nuclear force then its associated constant of Nature, ?s is subject to the stringent restriction:
Figure 11.5 The change in the probability for a samarium nuclear capture reaction to occur at different temperatures as we shift the position of the resonance energy.16 A zero shift means it has the same value as observed in nuclear reactions today.
{the rate of change of αs}/{the value of αs} < 10–19 per year
If only the electromagnetic interaction is changing with time then, because its contribution to the total samarium interaction rate is about 5 per cent, any rate of change of the fine structure constant, α, must obey the limit
{the rate of change of α}/{the value of α} > 5 × 10–17 per year And if only the weak force of radioactivity were to have varied over time, then the variation of its strength, αw, is bounded by
{the rate of change of αw}/{the value of αw} < 10–12 per year
These limits were far stronger than any limits on the possible time-variation of the constants of Nature that had ever been found before. The Universe has been expanding for about 14 billion years and so these limits, if taken at face value, are telling us that the fine structure constant cannot have changed by more than about one part in ten million over the entire age of the Universe. Previous observational limits were more than a thousand times weaker.
There are a few things that are immediately clear about these strong limits on the possible variation of the constants of Nature:
(a) They have a particular reach in time back to about 2 billion years ago, when the Oklo reactor formed, compared with 4.6 billion years for the age of the Earth and about 14 billion years for the expansion age of the Universe.
(b) If different constants varied simultaneously then the results might change.
(c) A particular simplifying assumption was made about the way in which the constants of Nature contribute to the neutron capture resonance energy.
(d) Some simplifying assumption has been made about the temperature inside the reactor when it was operating.
The unique probe of the constancy of constants that Oklo provides has ensured that Shlyakhter's brilliant observation has been investigated in much greater detail by others.18 The most detailed study has been carried out by Yasanori Fujii and his collaborators19 in Japan. Looking at Figure 11.6, we can see how a shift in the resonance energy (non-zero ? Er) plotted along the horizontal axis produces a change in the neutron capture probability, plotted up the vertical axis, that depends upon the temperature of the reactor. The allowed range for the neutron capture probability two billion years ago is between 85 and 97 kilobarns if the abundance of samarium is to agree with the range observed in the reactor sites. The various investigators of the samples agree that the temperature must have been somewhere between 200 and 400 degrees centigrade. Now, one can see from the curves drawn for these temperatures that there are actually two ranges of the shift ?Er that keep the capture cross-section within the allowed bounds:
–12 meV > ΔEr > 20 meV
taking the right-hand branch; and
–105 meV > ΔEr > −89 meV
if we take the left-hand branch.
The limit from the right-hand branch is a refinement of Shlyakhter's original result and leads to a more stringent limit on possible time variation of the fine structure constant if it is the only constant that is assumed to vary. The limit is and is about five times stronger than the earlier one. It allows there to be no variation at all because of the + 0.8 uncertainty in the inferred value. This uncertainty would need to be reduced well below + 0.2 in order for there to be believable evidence for any actual variation. However, if we take the left-hand branch result then it does not allow ΔEr to be zero and leads to the deduction that there has been a non-zero change in the value of the fine structure constant since the Oklo event, equal20 to
If one looks at the abundances of the other isotopic residues of the Oklo event then this second result might be excluded.21 But so far the data sample quality and uncertainties about the temperature in the reactor prevent us from ruling it out definitively.
It is also interesting to see the consequences of allowing the electromagnetic and strong nuclear force strengths to vary in time simultaneously. Typically, this leads to limits on the time variation of both ‘constants’ which are about as strong as those we have just given for the fine structure constant. But there is a peculiar situation, albeit looking rather contrived, in which the limits on variation are far weaker. If, for some unknown reason, the rates of change in the strong and electromagnetic interactions over 2 billion years are equal to within one part in ten million then the effects of the two constant changes cancel. The new limits are dramatically weakened to a level that would have been the case if there was no special neutron capture resonance at all:
Although this finely-tuned, one-in-ten-million chance for the possible variation of the electromagnetic and strong force constants might sound rather contrived, it is actually a prediction that they vary at exactly the same rate in a wide range of theories which attempt to join together the different forces of Nature, so this possibility should not be excluded as absurdly unlikely.22
‘the first nine digits after the decimal can be remembered by e = 2.7(Andrew Jackson)2, or e = 2.718281828 …, because Andrew Jackson was elected President of the United States in 1828. For those good at mathematics on the other hand, this is a good way to remember their American History.’
Edward Teller23
To most people the word radioactivity brings to mind a sentence in which there also appear words like accident, waste, leak, cancer or disaster. But without radioactivity we would not be here. The delicate sequence of processes that create the steady flux of solar energy that bathes the Earth is made possible by radioactivity. When the Earth condensed into its present mass of material about four and a half billion years ago it contained enough metals like nickel and iron at its core to sustain a significant magnetic field. Without it, we would have no life-sustaining atmosphere. The wind of electrically-charged particles that are continually blown away from the Sun's surface would have stripped our atmosphere away, just as they have on Mars where there is no magnetic shield. The Earth's magnetic field defends us against these invaders by deflecting them around the atmosphere.
Along with this life-sustaining inner core of iron and nickel, the primordial Earth also picked up enough radioactive elements, like uranium, to maintain a long period of heating by radioactive decays deep inside its interior. This inner engine played a key role in unlocking the Earth's geological potential. The subterranean furnace has stimulated continual editions of mountain building and plate tectonics, keeping the surface alive and changing in a way that provides a suitable habitat for land animals and amphibians.
When the idea that some of the traditional constants of Nature might be slowly changing was first suggested by Dirac and Gamow, many physicists realised that the constants that controlled radioactive decay must be crucial for the history of planet Earth. Any change in their past values would most likely upset a delicate balance and create too much or too little heating.
Radioactive elements act as clocks. Their ‘half-lives’ tell us the time required to halve their initial abundance. They fall into groups with half-lives that are billions, millions and thousands of years respectively.
Following the first attempts by Denys Wilkinson24 to get limits on the constancy of constants by these means in 1958, Freeman Dyson25 used the half-life of long-lived beta-decaying nuclei, such as rhenium187, osmium-187 and potassium-40 to place a limit on possible past variation of the fine structure constant from its present value. These three nuclei have very long half-lives that have been determined accurately by laboratory experiments and by comparison with the ages of meteorites. Given that the uranium-238 decay rate must have been within 20 per cent of its present value over the last 2 billion years, one deduces that
Similar studies of different decay sequences by other scientists26 led to other limits of a very similar strength. These limits were eventually superseded by evidence of the Oklo natural reactor.
‘This rock salt is over 200 million years old, formed through ancient geological processes in the German mountain ranges. Best before 04 2003.’
Product label27
The Oklo phenomenon may well not have been unique. The conditions needed to sustain chains of nuclear fission reactions are unusual but not in any way bizarre. It is possible that other natural reactor sites have been mined out unnoticed or lie awaiting discovery at other sites on Earth. Although there are other sites in Africa and in Colorado, USA, that display deficits of uranium-235 that might have been created by naturally occurring nuclear reactions, none is believed to be a natural reactor.
The discovery of these possible natural reactor sites is important not only for studies of the constants of Nature. They tell nuclear physicists important things about the future stability and confinability of nuclear fission products buried underground for very long periods of time. Maybe one day a piece of very careful chemical book-keeping will lead to a replay of the exciting sequence of investigations that unmasked the Oklo reactor.
If natural reactors can occur on Earth then why not elsewhere? It is tempting to speculate that a new source of life-sustaining heat energy has been identified which might play an unusual role in incubating biochemical evolution on other worlds. The astronomer Fred Hoyle28 once wrote a science fiction novel about the development of life on a comet that was initiated and sustained by natural nuclear reactions occurring within its core. Perhaps the search for extra-solar planets will discover a planet or a moon on which the Oklo phenomenon occurred on a vaster scale, heating up the interior for long periods of the planet's life and sustaining the development of complex bacterial life, before shutting down and leaving the planet dormant and superficially dead.
It is sobering to think that the time in the history of the Universe when life exists has dictated some interesting nuclear consequences for human life. We have seen how the different decay rates of the two uranium isotopes make uranium-235 relatively more abundant in the past. By the same token it will be relatively less abundant on planets like the Earth in the far future. During the last century we discovered that our planet's crust contains radioactive elements that enable nuclear bombs to be created with some technical skill if we refine the active uranium-235 isotope from the more abundant uranium-238. If humans appeared far earlier or far later on our planet than they did then their prospects for harnessing nuclear weapons would have been very different. Here is the prescient analysis of John von Neumann, one of the most remarkable scientists of the twentieth century, written at the dawn of the nuclear age:
‘If man and his technology had appeared on the scene several billion years earlier, the separation of uranium 235 [crucial for making bombs] would have been easier. If man had appeared later – say 10 billion years later – the concentration of uranium 235 would have been so low as to make it practically unusable.’29
We are the beneficiaries of many aspects of the Earth's interesting geology. The presence of heavy elements with interesting magnetic and radioactive properties has led to our understanding of these fundamental forces of Nature. Life on a pleasant, irrigated planet, bathed in the light of a well-behaved star, would be possible with nothing of nuclear or radioactive interest anywhere near its surface. But its inhabitants would be severely handicapped in their quest to understand the scope and richness of the forces and constants of Nature.
