AUSTRALIAN FRONTIERS OF SCIENCE, 2008
The Shine Dome, Canberra, 21-22 February
Quantum landscapes in nuclear fusion
by Dr Mahananda Dasgupta
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Mahananda Dasgupta has a PhD from the Tata Institute of Fundamental Research in Mumbai, India. Her research interests brought her to Australia where she worked as a Postdoctoral Fellow in the Department of Nuclear Physics at the Australian National University. She was awarded a Queen Elizabeth II Fellowship, and pursued her work in the field of fusion of heavy nuclei, developing new instrumentation and demonstrating the effects of the quantum properties of nuclei on the reaction outcomes. Nanda received the 2006 Pawsey Medal from the Australian Academy of Science for her breakthroughs in this field. |
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We deal in our everyday lives with macroscopic systems. They follow the laws of classical mechanics, which are basically Newton's laws. To use the illustration here as an example: we know where the tennis ball is and where the player is, and it is all deterministic.
The problem is that if I make the tennis ball into a very, very small object, like atoms or nuclei or electrons, then it is a completely different ball game, because they follow quantum mechanics. These atoms and nuclei and electrons do not behave completely like particles, but have wave-like properties. We talk of the 'probability' that we will find the nucleus here or the atom there, but we cannot deterministically say, 'This is exactly where it is.'
One of the amazing things about quantum mechanics, which makes it distinctly different from classical mechanics, is that the system is in what we call a coherent superposition of states. It basically means that the system can exist in a combination of all the possible individual states that the system can have.
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If this quantum system is isolated, that is all fine, perfect. But its interaction with the rest of the world, the rest of the system, which in this talk we shall call the 'environment', destroys this superposition and leads to an emergence of classical behaviour.
A key challenge currently in physics is to understand the effect of this environment and this quantum-to-classical transition. For example, quantum computers, which we hear about so much, rely on preserving coherence during the computation. And in order to make it into a success, what we need to find is ways to mitigate the decoherence effects, or the effect of the environment.
Collisions of atomic nuclei the subject of my talk today are unique, because nuclear energy scales are much different from those of atoms and molecules. So, effectively, they have no external environmental interaction (because of the difference in energy scales) and hence it is a unique probe to understand, or look for, the effect of coherence.
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After the previous session on plant disease I thought that when I say 'nucleus' people might think, 'Ah! The nucleus of the cell.' So I just want to make sure that we are talking about the right nucleus! We are now going from galaxies to fungi to an even more minute scale, that of inside the atom, 1/10,000 of that scale. At the centre of the atom there is a nucleus, which is the atomic nucleus. And that is the nucleus which I will be talking about.
This atomic nucleus is made up of protons and neutrons. Protons are positively charged, and the neutrons are neutral. Therefore, the nucleus has a net positive charge.
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When I bring two nuclei together in a collision, two positive charges will repel because of the electrostatic force. This is just like the two identical poles of a magnet not being able to be brought together because of the magnetic force. How does fusion occur, then? How can I even talk about fusion, when it means the two nuclei have to stick together?
An analogy is that if I put some Velcro at the end of the magnets and bring them together, force them together, then as they touch the Velcro will take over and they will stick.
In the case of the nucleus, the role of the Velcro is being played by the strong attractive force, which as David Jamieson very eloquently said, is one of the most challenging forces to understand. It is much stronger than the electrostatic force, and that is why nuclei which have two positively charged particles stick together to form a new nucleus.
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So the two players in this game are the attractive force and the repulsive force.
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The attractive and repulsive potentials together form a barrier. That is a very important concept in my talk today.
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On one side I have two nuclei, and I overcome the barrier, see the attractive potential pocket and fuse.
I know when I draw potentials, many people will go, 'Oh my God! Graphs and potentials! Can't handle that.' So, because I want to convey the concept of a barrier well, think about it like a high jumper. There is a barrier to get over to the other side, and you need a certain energy to go over the barrier and end in the land of fusion. So that is the barrier.
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Here we have the potential, the barrier. If I have enough energy I go over the barrier and all is well. But nuclei are quantum particles. So if I have energy lower than the barrier height, then in a classical system your tennis ball will just come back. But because of the wave-like properties that the nucleus has, it can tunnel through and be found on the other side of the barrier, even when its energy is not sufficient to overcome that. This is another amazing phenomenon in quantum mechanics, which is called quantum tunnelling.
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If I now use those principles of barrier and quantum tunnelling, and compare the theory with experiment, it looks pretty poor. This is a measurement of fusion cross-sections, which is related to the probability of fusion, plotted against energy, and there is a huge discrepancy. The log scale is displayed here, so it is a factor of 100 off a factor of 100! Obviously, there is something missing in the theoretical description.
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What is missing is that nucleus is a quantum system it is a many body quantum system and it has energy levels, excited quantum states. And the nuclei, as they are approaching, go into a linear superposition of all these possible states. That means these nuclei can simultaneously exist in all these possible states. (That is the peculiarity of quantum mechanics.)
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As a result, what happens is that we do not have just a single barrier; instead we have many barriers as the nuclei try to come together. So we need Olympians who are very well versed in quantum mechanics to win this event!
You may say, 'Oh great, good story. Do we believe it? Can this effect of coherence be probed?'
Yes, but it requires precision measurements and we have been able to see this effect by techniques which were pioneered by our group at the ANU.
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One of the most important, even essential, ingredients is generating the energetic nuclei. That is done by an accelerator, and this slide shows an aerial view of the Heavy Ion Accelerator facility at the ANU.
In a cross-sectional view of this accelerator you can see that it is an electrostatic accelerator with 15 million volts at its centre. That is what accelerates the nuclei, which start at the top. At the end of the acceleration, nuclei are travelling at 10 per cent of the velocity of light, or 30,000 kilometres per second. They come around and hit the target, and fusion reactions occur.
That is fine, but typically we might have one fusion event in a background of up to 10 billion scattered particles. One in 10 billion, that is what we need to detect, and that is not a very easy task.
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We have to have a specialised detector system, SOLITAIRE, which is shown here. It is a new generation detector system which separates the fusion product from the scattered beam, so that the fusion products go through to the detector and get detected. This was conceived and developed in-house at the ANU.
This picture also gives me the opportunity to acknowledge the fact, in relation to the experiments I am going to describe, that I have not done it all by myself. A team effort is involved in doing experiments of this scale.
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Here is another experimental set up. This is a detector which has been developed in-house, and which goes to form a part of the highly efficient fission detector array. These are the systems that we would use to detect the fusion products.
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So what do we see? Remember, we wanted to see many barriers. Are there many barriers? Is the story of coherence really true?
On the y-axis we basically have the second derivative of the cross-section, which is related to the probability of encountering a barrier; on the x-axis is energy. If we had just one single barrier, then we would get the dotted line, but the experimental data shows that is not the case. In fact, it shows there are two barriers in the first case here, and many barriers in the second case clear evidence of quantum coherence effect in fusion. (Whether there are two or many depends on the structure of the nuclei involved.)
These experiments, and those that followed, firmed up the evidence that quantum coherence affects nuclear fusion, and presented a paradigm shift in how people viewed fusion, leading to an understanding of what is called coupling enhanced quantum tunnelling, and development of a realistic model of fusion.
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Fusion, as already referred to earlier, is responsible for element formation in the universe. Hydrogen and helium were there at the beginning of the universe, but all the heavy elements were made from fusion reactions in stars. For example, hydrogen fuses to form helium in the sun, which generates energy and stabilises the sun against gravitational collapse. For heavier stars, helium can fuse to form carbon, carbon can fuse to form magnesium, and so on up to iron.
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Then there are no more energy-generating reactions with iron, and the star undergoes a huge gravitational collapse the star collapses. But nuclear matter is not infinitely compressible, so the star rebounds. And in the shock wave, the star basically explodes and dies, resulting in a supernova explosion in which elements formed in the stars are distributed throughout the galaxy. So each atom in our body has gone through 100 to 1000 star generations, and we are made up of stardust.
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Elements beyond iron are formed in that explosive environment, but there is very limited knowledge about those reactions. The reason is that it involves reactions of nuclei with very unusual proton to neutron ratios, and they are unstable and not found on Earth. For example, we are all familiar with carbon-12, but there are nuclei like carbon-22, with 16 neutrons, 10 more neutrons than the normal carbon. This represents an extreme state of matter at the limits of existence. But new accelerators worldwide, which can deliver beams of unstable nuclei, are just coming up. They will allow us to study the structure of these nuclei at the limits of existence and understand their reactions.
At the ANU we are developing a capability to produce helium-6 beams, which will be a first in Australia. We will use this to study the interface between classical mechanics and quantum mechanics.
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To come back to the naturally occurring elements: the heaviest element naturally found on Earth is uranium. We all know about uranium; we are making some money out of it. It is packed with 92 protons in a tiny volume, and there is enormous electrostatic repulsion. The nuclear force holds it together just about, because if we add more protons to the nuclei the heavier element becomes more and more unstable, and the nuclei live for a shorter and shorter time. So even if some heavy elements were created in the supernovae ages ago, none would be left. They would have broken apart because of the repulsion.
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So, does uranium represent the boundary of existence of heavy elements? The chart of nuclei on this slide shows the number of protons versus the number of neutrons. This summarises all the nuclei that we know. Each black square represents one isotope of a stable nucleus. All the light ones are unstable nuclei. The nuclei in the top left of the chart are unstable and not found on Earth, and this is called the Sea of Instability. Uranium is sitting on this 'land' of stable elements. If I delve into the Sea of Instability, do I expect to find any heavy nuclei, or is it all going to be unstable? Well, you are in for a surprise.
At the top right of the chart you see a predicted island of superheavy nuclei. These predictions have come about because of the understanding of nuclear structure effects, and they are stabilised by surprise, surprise quantum effects.
We have just about reached the shores of this superheavy nuclei 'island', and the quest for superheavy elements has led us to the discovery of new elements.
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So the periodic table of elements as we know it is on the increase.
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Here you see an element with 111 protons, called Roentgenium, being added to the periodic table about a year and a half ago. Last year physicists in Switzerland chemically characterised element 112.
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But these elements are very hard to make. The reason is that as I bring two nuclei to come together to form a new element, they might stick together and rotate around, but the enormous electrostatic repulsion can break them apart again.
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So when I collide two nuclei to form a heavy element, which path it will take whether it will break apart or form a heavy element depends on many variables. Our current research at the ANU aims to pin this down.
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This slide shows a graph of two different reactions aiming to form the same compound nucleus. This is mass (x-axis) versus angle (y-axis). What the big blob in the left-hand graph shows is that the fusion has taken place, the nuclei have stuck together long enough for heavy element formation to have taken place. In the right-hand case, however, there is a whole slew of particles which are between the target and the projectile. This shows that the nuclei did not stick together long enough.
Understanding these results needs a theoretical modelling of a many body quantum system going through a potential landscape which depends on many variables, and this is a very common problem encountered in many areas of physics.
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When we form a new nucleus, we have completely rearranged the system in an irreversible manner. The problem is: how do we go from quantum superposition to irreversible outcomes?
What we have proposed recently is that quantum tunnelling in fusion is a clean way to investigate the onset of irreversibility.
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What we see here is the calculation of the standard model of fusion, and the data this is fusion cross-section (y-axis) versus energy (x-axis). And as we go further and further below the barrier, the data falls lower and lower compared with the calculations. We are thinking at the moment that it is because of a loss of quantum coherence as the nuclei start overlapping. The lower in energy we go, the more overlap there is, because the inner turning point is moving to smaller separations.
Is that leading to an emergence of classical behaviour? In the classical limit, nuclei would behave like tennis balls and fusion will not take place (just like the tennis ball bounces back if its energy is below the barrier). The fact that the fusion measurements fall below the expectations based on quantum tunnelling may be implying that the system becomes increasingly classical as the overlap between nuclei increases.
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We are currently working to include irreversibility in quantum description in a self-consistent manner, and in this we are collaborating with quantum information theorists from the University of Queensland.
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To summarise: I hope I have given you a flavour of some of the frontier research in nuclear reaction dynamics. It has been an amazing time to work in this area, because it has thrown up experimental challenges and theoretical challenges, and experiment and theory have gone hand in hand in recent years to allow us to answer questions about fundamental quantum mechanics.
What I have shown you is that the reaction dynamics is critical in the formation of elements in the cosmos, as well as in the laboratory where we try to synthesise new heavy elements.
Our recent results show that not only do we see effects of coherence but we may be able to investigate effects of decoherence in quantum tunnelling in fusion.
