Eur. Phys. J. A (2026) 62: 108
https://doi.org/10.1140/epja/s10050-026-01856-x

Review

Theoretical studies of $\alpha$ clustering in nuclei and beyond

¹ Department of Physics, University of Tokyo, Hongo 7-3-1, 1130033, Bunkyo-ku, Tokyo, Japan
² RIKEN Nishina Center for Accelerator-Based Science, Hirosawa 2-1, 3510198, Wako-shi, Saitama, Japan
³ Department of Physics, Florida State University, 311 Keen Building, 32306-4350, Tallahassee, FL, USA
⁴ Department of Physics, Osaka Metropolitan University, 3-3-138 Sugimoto, 558-8585, Osaka, Osaka, Japan

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 26 February 2026
Accepted: 7 April 2026
Published online: 1 June 2026

Abstract

This article comprises three sections after an introduction. Section 2 starts with a quick review of the results of ab initio no-core shell model calculations by Monte Carlo Shell Model on light nuclei. It is shown that $\alpha$ clustering arises in such first principles calculations for $_{}^{8,10,12}$Be and $_{}^{12}$C with the Daejeon16 and JISP16 interactions. The $\alpha$ clustering occurs even in well bound states such as the ground state of $_{}^{12}$C. The Hoyle state is shown to be dominated by $\alpha$ clustering in triangular configurations. The crossover between clustering and nuclear matter is demonstrated. As the ground and Hoyle states show strong deformations, they are also good cases to investigate rotational excitations. As an original work, the recently proposed fully quantum (mechanical) formulation for deformation and rotation is extended to cluster or molecular states. Dual rotational modes are proposed: compact-object rotation and distant-object rotation. The former is found in many heavy nuclei, whereas the latter can be found for clustering states in Be and C isotopes. While $_{}^8$Be is a transparent example for the latter, $_{}^{12}$C is a rare example that both modes appear in different states of the same nucleus, giving another novel significance to the Hoyle state. The duality of rotation by compact-object and distant-object rotations is a visible outcome of the hierarchy by the cluster formation, placing $_{}^{12}$C on the border. Atomic molecules and hadrons can be viewed in terms of this duality. Possible relevances to fission is mentioned. Section 3 presents a general framework for an extended no-core shell model with cluster–nucleon configuration interaction, combining traditional shell-model–like configurations with explicit microscopic configurations representing cluster degrees of freedom. This approach offers a complementary perspective to the strategy discussed in the other sections. The section reviews the microscopic origins of cluster substructures in light nuclei, emphasizing how nucleonic degrees of freedom, nucleon–nucleon interactions, and continuum coupling naturally extend the traditional shell model into configuration-interaction frameworks that incorporate clustering and reaction dynamics. Both methodological developments and applications are discussed, including clustering in well-bound states as well as reaction processes involving $\alpha$ clusters. Section 4 presents that although the cluster structure is robust in Be-C nuclei, some jj-coupling shell model components are mixed with clustering components in the ground state of $_{}^{12}$C. This is a different feature than in the cases of the Be isotopes. Using the antisymmetrized quasi cluster model (AQCM), we can clearly model this competition between the cluster and shell components. The spin-orbit interaction is key to realizing the shell structure and contributes more to the $_{}^{12}$C case than to the $_{}^8$Be case due to closer $\alpha$-$\alpha$ distances in the former case, thanks to attraction among the clusters. Section 5 presents remarks and prospects transcending the whole article, besides summarizing discussions within Sects. 2–4.