A century ago, physicists did not have a satisfactory explanation of the process that powers the sun. Some had speculated that it was a giant ball of burning coal - leading to the rather alarming conclusion that it would soon burn out! Others argued that the heat was the result of the gravitational contraction of a giant ball of gas. Although this led to a longer calculated lifetime, it was still nowhere near long enough to satisfy geologists and biologists, who called for hundreds of millions of years to explain geological structures and the evolution of life on Earth. It wasn’t until the 1930’s that the mystery was finally solved, when physicists discovered the true source of the sun’s energy – the fusion of hydrogen nuclei to form helium.
Despite great progress since then, the mechanism of fusion of heavier nuclei is still not properly understood, and nuclear scientists today are working hard to unlock the mysteries of this fundamental process. Scientists at ANU have recently suggested that problematic experimental observations may be a result of the process of fusion being at the boundary between classical physics, where Newton’s laws of motion hold sway, and the stranger world of quantum physics.
First, let’s look at the fusion of two hydrogen nuclei in a classical way. Coulomb’s law of electrostatics tells us that the two positively charged nuclei will repel each other more strongly as they approach closer. If they are moving towards each other slowly, this repulsion will cause them to bounce apart long before they touch. If their velocity is high enough, they will have enough energy to overcome the Coulomb barrier (think of trying to roll a ball over a hill) and begin to overlap. At this point, the hugely strong but very short range attractive nuclear force takes over, forcing the two to fuse, forming a single nucleus (imagine two drops of water touching and merging into one).
This classical picture sounds quite straight forward, but in the Sun, when you plug the numbers in, it doesn’t lead to fusion! The thermal velocities at the centre of the sun are not sufficient for hydrogen nuclei to overcome their Coulomb barrier and fuse. And yet, as we see every day, the sun does shine! So how is this possible?
The answer lies in quantum mechanics. Quantum theory tells us that the motion of tiny particles like nuclei can be thought of as having a wave-like property. The wave-function is a mathematical expression that tells us the probability of finding the particle at any given point in space.
One of the interesting things to come out of the mathematics of wavefunctions is that they don’t have sharp discontinuities. In other words they do not abruptly drop to zero at a barrier. This means that the wavefunction of a particle outside a potential barrier actually extends under the barrier, where classically, its energy is negative! The wavefunction falls off exponentially under the barrier, so depending on its thickness, there is a small but real probability of finding the particle inside the barrier. This means that every now and again, a particle can pass through a classically impassible barrier, a process known as quantum tunnelling.
Quantum tunnelling is what happens within the sun. A minute proportion of the collisions of hydrogen nuclei lead to fusion, creating helium nuclei and releasing vast amounts of energy in the process.
One of the key ideas in quantum mechanics is superposition, meaning that until a measurement is made a quantum system can exist in all possible states at the same time. The process of measurement forces the system to make a transition from the many simultaneous possibilities to a single outcome. One of the challenges of modern physics is to understand the transition from superposition of states (quantum world) to a single definite outcome (classical world).
Drs Mahananda Dasgupta and David Hinde are two nuclear physicists at the ANU exploring the fusion process, and the light it may shed on the shadowy interface between the classical and quantum worlds.
The nucleus is a unique place in nature because the nuclear force that binds it together is so much stronger than any of the other 3 fundamental forces of nature (weak nuclear, electromagnetic and gravitational forces) that it overwhelms them. This means the neutrons and protons inside a nucleus are effectively isolated from all external influence.
“The nucleus is a fascinating object because it’s so thoroughly isolated. Each nucleus is a miniature universe in itself.” Dr Hinde explains. “Prior to the moment of fusion the protons and neutrons are completely unaware of anything outside their own nucleus, then suddenly a whole new universe crashes in and all the particles re-organise themselves in a frantic burst of quantum activity.” The nuclei are in a quantum superposition prior to fusion, but the reorganization of all the constituents of the two nuclei is the “measurement” that leads to a definite outcome - fusion. The question is, where does this measurement process start?
To study this Drs Dasgupta and Hinde use Australia’s largest and most powerful heavy-ion accelerator at the ANU, with accelerating voltage of over 15 Million Volts. A precisely defined beam of highly energetic nuclei are directed onto a thin target foil, where they can fuse with nuclei in the target to create heavier elements. After fusion, these new heavier nuclei evaporate some neutrons, and maybe protons, emit a number of characteristic gamma rays, and finally often decay by emitting an alpha-particle (also through quantum tunnelling!). “You can’t see the fusion directly but you can detect the products emitted following fusion.” Dr Dasgupta says.
However even the tell-tale fusion products are not easy to observe. The space between nuclei is vast even in seemingly solid materials, so the probability of a head on collision between two nuclei is miniscule. For every direct hit there are millions of glancing collisions that simply scatter nuclei out of the beam, resulting in an intense cone of scattered nuclei mixed with a few fusion products, all going forwards. To separate the two, the team have developed a powerful superconducting solenoidal separator that generates a strong magnetic field. Because the charged particles are deflected by the magnetic field according to their mass and velocity, it’s possible to focus the fusion products on their detector, and divert the scattered beam particles onto a stopper.
One of the most interesting results to come from this work so far is that the observed quantum tunnelling can be 10 times smaller that predicted by theory. Dr Dasgupta believes that this may be due to quantum decoherence.
“As two nuclei approach each other they each exist as many possible quantum states superimposed together. However when they meet and begin to combine these possibilities have to condense into a single measured reality.” She explains, “So what we think we’re seeing is a transition from quantum to classical behaviour during the tunnelling process. And of course tunnelling is only possible in the quantum world so the transition to classical behaviour may be strongly reducing the tunnelling effect.”
The nucleus makes a particularly interesting laboratory for quantum physics because it’s such a pure and isolated system. An improved knowledge of how tunnelling nuclei behave may well lead us to a better understanding of what the mathematics of quantum mechanics actually mean in the real world.