– One example of this application is determining the mass of nuclei immersed in a superfluid neutron liquid – explains Prof. Piotr Magierski. – As the nucleus moves, it 'drags' part of the neutron liquid along with it, increasing its effective mass compared to its mass in a vacuum. At higher speeds, viscosity emerges, driven in part by the generation of quantum vortices. Conducting a quantitative analysis of these phenomena is essential for understanding the properties of neutron star crusts.

In this way, the researchers determined the effective mass of a nucleus, acquired as a result of interactions between nuclei and the superfluid Fermi liquid, enabling the study of the structure and dynamics of these stars' interiors.

– One of the densest forms of matter in the universe is found in neutron stars – explains Daniel Pęcak, PhD. – To achieve a similar density on Earth, we would need to compress the entire Palace of Culture and Science into a volume comparable to a single sugar crystal. Producing such nuclear matter in laboratory conditions at low temperatures remains beyond our current capabilities, which significantly hinders the study of its properties.

Our researcher emphasizes, however, that despite this, the matter continues to spark great interest due to its extraordinary properties, which are crucial for understanding the dynamics of neutron stars, observed astronomical phenomena, and fundamental aspects of physics.

– For example, the microscopic properties of nuclear matter determine how quickly a neutron star cools or how its rotation period changes – explains Daniel Pęcak, PhD. – Importantly, both the cooling rate and the rotation period can be measured with precision through astronomical observations."

Bridging the gap

Since conducting direct experiments on nuclear matter is impossible, numerical simulations have become essential. Currently, there is no open-source software available to researchers that accounts for key quantum effects. The authors of this study address this gap by providing a tool that enables numerical experiments on the inner dynamics of neutron star crusts, incorporating their superfluidity.

Researchers apply the density functional theory, a methodology well-established in various fields such as quantum chemistry and solid-state physics. By utilizing advanced mathematical approaches, this method captures the behavior of thousands of interacting particles, reducing their complex relationships to elegant simplicity – as if they were entirely independent of one another. This technique has been under continuous development at the Division of Nuclear Physics at WUT's Faculty of Physics. The authors demonstrate its effectiveness by addressing the problem of a nucleus strongly interacting with a superfluid Fermi liquid. In this scenario, the interactions modify the effective mass of the nuclei, similar to the case of electrons in semiconductors. Precise microscopic knowledge of the effective mass can have a significant impact on the global properties of neutron stars, such as their transport properties and cooling rate. The calculations were carried out within the framework of the LUMI, computing grant, utilizing the most powerful supercomputer in Europe.

In the WBSk package developed by our physicists, the numerical engine has been separated from the model description, allowing it to be flexibly adapted to various specific research problems. The absence of assumptions regarding geometry gives the tool exceptional versatility and broad applicability. Thanks to this innovative software, the scientific community can gain new opportunities for effectively studying the inner crust of neutron stars.

The software enables the testing of various microscopic models while offering a deeper understanding of the mesoscopic and macroscopic properties of neutron stars—properties that can be validated through astronomical observations.

The article by physicists from WUT titled "Time-Dependent Nuclear Energy-Density Functional Theory Toolkit for Neutron Star Crust: Dynamics of a Nucleus in a Neutron Superfluid", developed in collaboration with the Belgian team from Université Libre de Bruxelles, is available at this link.