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The Rigakubu News
The Rigakubu News, Nov. 2025.
Research Student Communicates to Faculty >
When high-density nuclear matter turns into quark matter
Hiroyuki Tajima (Assistant Professor, Department of Physics)
Neutron stars, extremely dense celestial objects, have attracted attention as the “only natural laboratory for high-density matter” in nuclear physics. As their name suggests, the majority of a neutron star is thought to consist of a sea of neutrons. At the same time, observations of gravitational waves and X-rays suggest that, in the innermost regions of the star, neutrons may dissolve and quarks can move freely. However, it remains unknown how a collection of neutrons transforms into a collection of quarks as density increases. Understanding this process is a critical problem that spans both astrophysics and nuclear physics. In this study, we approached this mystery from the perspective of condensed matter theory.
What happens when a material is compressed to extreme densities? If you press an onigiri (rice ball) tightly, it compresses easily as long as there are gaps between the grains of rice, but eventually, the grains break down and the rice turns into a sticky mass. This is not unique to onigiri; similar transformations occur when materials around us are compressed to extreme densities. Atomic nuclei are composed of protons and neutrons, which themselves are made of elementary particles called quarks. When a cluster of neutrons is compressed to extremely high densities, the neutrons gradually break apart, giving rise to a collection of quarks—so-called quark matter.
The density of atomic nuclei is already extremely high, about 3 × 10¹⁴ g/cm³ (to give an analogy, compressing a 100 g onigiri to the size of a sugar cube would contain roughly three trillion onigiri). Recent studies have revealed that even higher densities can exist inside certain exotic celestial objects—namely, neutron stars. Observations indicate that neutron stars have radii of about 10 km, yet can contain masses up to twice that of the Sun. Knowing both the radius and the mass allows us to infer information about the internal pressure and density of the matter, and the central density is expected to reach several times that of atomic nuclei. At such densities, the average distance between neutrons becomes smaller than the size of a neutron itself—much like rice grains crushed in a highly compressed onigiri. It is therefore not surprising that quark matter could emerge in the core.
When matter changes its state, a phase transition usually occurs. If the neutron clusters in the core transform into quark matter, could this be considered a phase transition? Interestingly, observational data from neutron stars suggest that the transition may not be a sharp phase change, but rather a continuous crossover. Moreover, the speed of sound is predicted to reach a maximum in the intermediate density region. To clarify this mechanism, it is necessary to use a theoretical framework capable of describing matter at the level where three quarks combine to form a neutron, and to investigate the properties of such matter.
In this study, we approached the problem using insights from condensed matter physics. In that field, a phenomenon known as the BCS-BEC crossover describes a continuous transition between two distinct states: superconductivity and Bose-Einstein condensation. We noticed a similarity with the neutron-to-quark transition. Explaining the BCS-BEC crossover requires considering the continuous process of molecule formation and dissociation—so-called “fluctuations.” Inspired by this, we constructed a theoretical framework that incorporates fluctuations in the formation and dissociation of neutrons from three quarks. By calculating the speed of sound within this model, we indeed observed that it becomes faster in the intermediate density region. We hope that this result will serve as a catalyst for further interdisciplinary research on neutron stars.
The results of this study were published as H. Tajima et al., Phys. Rev. Lett. 135, 042701 (2025).
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Conceptual diagram of matter in the core and outer regions of a neutron star, and the density dependence of the speed of sound. The composite particle formed by the binding of three quarks, represented by primary-colored circles, corresponds to a baryon (such as a neutron).