Skyrmion-Skyrmion Scattering and Nuclear Physics

To understand a complex system such as the world we live in, it is useful to understand its parts. An atom, for example, consists of electrons and the atomic nuclei, which in turn consist of protons and neutrons. As particle accelerators have revealed, protons and neutrons are also made up of smaller particles, each one contains three quarks. And so, now that we know the protagonists, we need to understand how they interact. Apart from gravity, there are three interactions: the electromagnetic interaction which acts only on charged particles (such as electrons and protons); the weak interaction which only affects certain particles and is very weak indeed; and the strong interaction which holds atomic nuclei together. The strong interaction is much stronger (and much more complicated) than the other two, but it falls off very rapidly with distance. In the theory of the strong interaction known as quantum chromodynamics (QCD), quarks interact via yet another type of particle called gluons. At the very high energies found in particle accelerators such as LHC in Geneva, QCD explains experimental findings to an amazing accuracy. However, at lower energy levels, quarks like to stick together, either in threes to form protons and neutrons or in twos to form particles known as pions. As a consequence, a single quark can never be observed on its own. This means that QCD becomes very complicated at low energies and it is extremely difficult to calculate the properties of a proton from QCD.An alternative approach to this problem was devised in 1961 by the British physicist Tony Skyrme (1922-1987), before QCD was discovered. Skyrme proposed a theory which involves only the particles that are directly observable, the protons, neutrons and pions. The theory is very elegant, since protons and neutrons are described as topological solitons, which can be thought of as knots in a field of pions. In Skyrme's honour, these solitons are known as Skyrmions. In 1979, the American theoretical physicist Edward Witten showed that the Skyrme model captures the essential features of QCD for low energies. This means that we can use the Skyrme model to describe the phenomena in nuclear physics.In standard nuclear physics, atomic nuclei are bound states of protons and neutrons under rules which have to be determined for each case. This approach gives accurate results but does not provide a unified picture coming from first principles such as QCD. The Skyrme model lies between standard nuclear physics and QCD, and thus provides a different perspective on nuclear physics experiments.Although the Skyrme model is much simpler than QCD, many difficulties remain. Since protons and neutrons obey the laws of quantum mechanics, the Skyrme model with its Skyrmions also needs to be quantized. There are some technical issues (namely the calculation of what are called Finkelstein-Rubinstein constraints) which I have recently resolved. Using these techniques masses and excitation energies of atomic nuclei have been calculated and achieved remarkable qualitative agreement with nuclear physics. Despite its motivation from physics, this project is firmly rooted in mathematical physics using sophisticated mathematical tools devised by pure and applied mathematicians.A vast amount of nuclear physics experiments is concerned with the scattering of atomic nuclei - for example hitting a helium atom with a proton and measuring how the atomic nuclei break up. Such experiments can be compared to Skyrmion-Skyrmion scattering, an area of research which is currently in need of development. The aim of my project is to use both analytical approximations and numerical calculations to understand Skyrmion-Skyrmion scattering. There are early indications that the Skyrme model can help us to make experimental predictions in situations that are difficult to address with the standard techniques of nuclear physics.

My project is about using Skyrmion-Skyrmion scattering to describe the scattering of atomic nuclei. The UK is internationally leading in the field of topological solitons, and my work will have a big impact in the soliton community. The project is highly interdisciplinary, addressing problems in pure mathematics and numerical analysis. So, there will also be a lot of interest from the mathematical community. The main aim of the project is to use the Skyrme model to calculate the likelihood of various scattering events and compare the results to nuclear physics experiments. If these calculations were successful, this could have a major impact on nuclear physics. Obviously, having a better understanding of nuclear physics is of great practical importance for example for the safety of nuclear power. The project will give a PDRA the opportunity to further develop his numerical and analytical skills and become an expert on topological solitons and their application. The project will also give rise to interesting PhD projects which will further build knowledge in this area and contribute to the UK continuing to be a world leader in this field. Finally, the area of topological solitons is of a particular beauty both in terms of visualizing the various field configurations and in terms of the geometric concepts involved. This lends itself to promoting science in schools and via general talks to non-specialists.