Clustering in nuclei and hadrons

Atsushi Hosaka; Yoshiko Kanada-En’yo; Yasuhiro Yamaguchi

doi:10.1140/epja/s10050-025-01530-8

2023 Impact factor 2.6

Hadrons and Nuclei

Clustering as a Window on the Hierarchical Structure of Quantum Systems

Open Access

Eur. Phys. J. A (2025) 61: 103
https://doi.org/10.1140/epja/s10050-025-01530-8

Review

Clustering in nuclei and hadrons

Atsushi Hosaka¹^,2^a, Yoshiko Kanada-En’yo³ and Yasuhiro Yamaguchi⁴^,5^,6

¹ Research Center for Nuclear Physics, Osaka University, 567-0047, Ibaraki, Osaka, Japan
² Advanced Science Research Center, Japan Atomic Energy Agency, 319-1195, Tokai, Ibaraki, Japan
³ Department of Physics, Kyoto University, 606-8502, Kyoto, Japan
⁴ Department of Physics, Nagoya University, 464-8602, Nagoya, Japan
⁵ Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, 464-8602, Nagoya, Japan
⁶ Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, 351-0198, Wako, Saitama, Japan

^a hosaka@rcnp.osaka-u.ac.jp

Received: 6 November 2024
Accepted: 1 March 2025
Published online: 13 May 2025

Abstract

Clustering phenomena in hadron and nuclear systems are overviewed. Because the energy scales for hadron and nuclear systems are not very much different, we can apply similar ideas and methods for the study of the seemingly different two systems, with the key ingredient, cluster. Once clusters are formed, they develop low lying excitations near the threshold if suitable interaction is available. This is a universal phenomenon which has been known as the threshold-rule. For nuclear systems the most established is the alpha ( $α$ $\alpha$ -)cluster which is the nucleus of $^{4} He$ $^4\textrm{He}$ . How the $α$ $\alpha$ -clusters develop in nuclei of light-medium mass region, typically $^{12} C$ $^{12}\textrm{C}$ is discussed in a microscopic manner based on the antisymmetrized molecular dynamics. The evidences of such clustering in some static properties of nuclei and scattering phenomena are discussed. Similar clustering phenomena occur for hadrons, where quark clusters are developed in either colored or colorless channels which are considered to play an important role for exotic hadrons of multi-quarks. In particular colorless hadronic clusters can be good constituents to form molecular-like structure near threshold regions.

Communicated by Maria Borge.

Yoshiko Kanada-En’yo and Yasuhiro Yamaguchi contributed equally to this work.

© The Author(s) 2025

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