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Nuclei Using Topological Solitons

Periodic Reporting for period 1 - NUTS (Nuclei Using Topological Solitons)

Reporting period: 2016-10-01 to 2018-09-30

Atomic nuclei contain protons and neutrons, which in turn consist of quarks held together by the strong force. One of the major outstanding problems in modern nuclear physics is to calculate the properties of nuclei directly from the fundamental theory of the strong force, quantum chromodynamics (QCD). Among others, this issue was address by the British physicist Tony Skyrme more than half a century ago. His proposal was based on a nonlinear object known as a topological soliton —a particle-like solution of a nonlinear wave equation, where stability is due to a topological twisting or winding. In this context, the relevant topological soliton was called Skyrmion in his honour and it has the interesting feature that the associated topological number can be identified with the baryon number.

Hence, Skyrmions provide a novel approach, but despite decades of research the success of Skyrmions has been limited by two crucial failings. Firstly, Skyrmions predict atomic nuclei that are bound together too tightly to reproduce experimental results. Secondly, Skyrmions predict intrinsic shapes for nuclei that are often too symmetric and fail to match the clustering of light nuclei, in which molecular-like structures appear. The main objective of the proposal is to improve current models of Skyrmions, by including more complicated features that are usually neglected, with the aim being to ameliorate the above main failings. This novel approach builds a bridge between the worlds of high energy particle physics and nuclear physics that will be important for making predictions about experimentally unknown nuclei and matter under extreme conditions, such as in the interior of neutron stars. This project has been successful by showing that the inclusion of a type of subatomic particle (called a rho meson) that is usually neglected in studying Skyrmions, indeed addresses the main problems mentioned above and significantly improves the match to experimental data.
The procedure to successfully conduct the project was clear and it involved the acquisition of the transferable skills of numerical calculations, more concretely with the writing of parallel numerical codes using MPI (Message Passing Interface) to be run on Hamilton, the Durham University HPC cluster. Due to the ambition of the enterprise, a solid basis in both numerical calculation and MPI language was necessary. It is for this reason that an important part of the fellowship was spent in ensuring both skills. Indeed, as a check, the main results of the usual Skyrme model as well as its 2 dimensional version were successfully reproduced by a parallelised code.

The project aim was delivered in two steps giving rise to two novel papers in important journals (one still to be published). As it was also done in the past with the standard Skyrme model, we studied, at the initial stage, the inclusion of the rho meson for massless pions. This surprisingly decreased nuclear binding energies from the excess appearing in the standard description to values less than 4%, moving Skyrmion theory closer to experimental data. Then, the pion mass was included in the model with the outstanding result of the cluster structure appearance. This can be seen in the figure bellow, where the a) subfigure corresponds to the standard version of the model with very symmetric configurations while the c) subfigure shows the cluster structure arising with the inclusion of the rho meson. In addition, a comparison of nuclear masses within the two models to experimental data is included in b).

The importance of the project undertaken has allowed to disseminate the results worldwide with the attendance to conferences and workshop not only in UK but also in Poland or Brazil. In addition, seminars as invited speaker have been delivered in countries like USA or Japan. The audience was within the “Skyrmion community” in some cases, with other talks given to a more general public from particle and nuclear physics and even condensed matter physics, promoting a fruitful exchange among different fields.
Currently, the extension of the Skyrme model by the introduction of the rho meson has been successfully applied to nuclei with baryon numbers from 1 to 8 besides Carbon-12, where the success of the standard theory to obtain the ground state and the famous Hoyle state configurations is maintained. The important outcome of this project, dealing with the two main drawbacks of the Skyrme model mentioned above, can boost and encourage the “Skyrmion community” to further investigate this direction where the inclusion of the rho meson has been shown to play a key role in the description of small nuclei.

It is also expected that both behaviours (better binding energies and cluster structure) will remain when studying nuclei with higher baryon number. This may be a path to follow together with the study of nuclear matter under extreme conditions and its implications in thermodynamics and neutron stars. Further research in the topic will allow a better understanding of the link between QCD and nuclear physics which will be important for the possibility of realistic predictions and where collaboration with nuclear physicists will be welcome.
A comparison of Skyrmions in the standard Skyrme model and the extended version with rho mesons.