TOPTIER Theory for Rare Isotopes

TOPTIER(TOP-Tier Platform in Extreme Rare Isotope Science) theory primarily aims to conduct internationally competitive and leading theoretical research in nuclear physics by developing both ab initio approaches and phenomenological methods. Given the nature of nuclear theory related to rare isotopes, it is evident that producing worldclass research achievements in theory is, in many cases, difficult without fair collaboration with experiments. While groundbreaking results in nuclear theory itself—independent of experiments—are also important, such achievements will ultimately be validated through collaboration with experimental research, due to the inherent characteristics of the field.

A nucleus, consisting of nucleons governed by quantum mechanics, exhibits a wide range of structural and dynamical properties. Understanding the mechanisms by which nucleons assemble to form nuclei with exotic characteristics remains a fundamental problem in nuclear physics. This issue has received increasing attention in recent years, driven in part by the development of advanced rare isotope beam facilities that enable the production of nuclei far from stability.

Exotic nuclei manifest a variety of phenomena, including changes in magic numbers, shell evolution, the emergence of giant halos, and shape decoupling between the core and halo. A central challenge for nuclear theory is the development of reliable and predictive frameworks capable of describing these properties and of constraining unknown nuclear characteristics from newly measured observables. In parallel, we will investigate the potential of emerging computational paradigms—such as quantum computing and artificial intelligence—to address key theoretical and computational challenges in nuclear physics.

We now briefly summarize the progress and perspectives of the TOPTIER project in theoretical research to date. During the TOPTIER kick-off meeting, held at Seoul National University in December 2024, theory members from Japan and Korea actively discussed physics topics suitable for immediate pursuit in the initial phase of the collaboration. The “initial” topics selected include:

• Reaction theory:

Collaboration in research on direct reactions involving unstable nuclei, and analyze the reactions measured at RAON and RIBF, such as (p,2p) and (p,pn) reactions.

• Large-scale shell model for mass, moments and spectroscopy:

Perform large-scale shell model calculations using a supercomputer. Discuss the spectroscopy of unstable nuclei based on comparisons with experimental data from RAON/RIBF.

• Density functional theory and its applications in astrophysics:

Conduct systematic research on unstable nuclei based on the density functional theory. We aim to develop density functionals using data such as masses, nuclear radii, and lifetimes measured at RAON/RIBF, and to enhance nuclear data necessary for nucleosynthesis simulations.

• Nuclear clusters in nuclei and nuclear matter:

Discuss alpha decay and cluster decay of unstable nuclei, and cluster formation in finite and infinite nuclear matter based on microscopic theories. Based on these insights, we also discuss the nuclear matter equation of state.

To initiate practical collaboration on the selected topics, we organized the “Top-Tier Comprehensive Lecture Series: PIKOE Code & KSHELL Code” at IBS in Daejeon from February 17 to 21, 2025. During this school, two experts from Japan delivered lectures on nuclear reaction theory, focusing on knock-out reaction calculations using the PIKOE code, as well as large-scale shell model calculations employing the KSHELL code. To further foster collaborative efforts among TOPTIER theory members working on exotic nuclei, we also hosted the “TOPTIER Focus Program: Cutting-Edge Nuclear Theories for Exotic Nuclei” at IBS in Daejeon from April 21 to 22, 2025. This brief meeting served as the practical kickoff for TOPTIER theory collaborations. Moving forward, we plan to organize extended meetings to deepen and advance the collaborative work initiated during this program, including active discussions on potential collaborations between theory and experiment. As a result of these collaborative efforts, we have begun to produce noteworthy scientific outcomes, one example of which is presented in the figure.

The figure shows the triple differential cross sections of ⁴⁰Ca(p, 2p)³⁹K for the (3/2)⁺ ground state knockout reactions at E_lab = 197 MeV compared with the experimental data. Here, SP_WS refers to single-particle states obtained from a Woods–Saxon potential, and SP_RCHB to those from the Relativistic Continuum Hartree–Bogoliubov(RCHB) theory. KD(Koning-Delaroche) and EDAD1(Energy Dependent and A Dependent) denote phenomenological optical potentials, while DF(Double-Folding) represents a double-folding potential. To input the single-particle states from RCHB into the PIKOE code, we performed a non-relativistic reduction. The main contributors to this project are Prof. Kazuki Yoshida (Osaka University), Dr. Yixin Guo (IBS), and Dr. Myunghee Park (IBS, Ewha Womans University).

In addition to the topics mentioned above, we plan to further broaden the scope of the TOPTIER theory program. Examples of such extensions include the time-dependent relativistic Hartree–Fock method and the development of shell-model interactions.

We will also explore the application of quantum computing to problems in nuclear physics, particularly those involving exotic nuclei. For large systems, computational costs increase exponentially, making exact calculations with classical computers virtually impossible. Quantum computers are the only means that can potentially overcome this limitation. At TOPTIER, we also plan to research quantum circuits for diagonalizing Hamiltonians of nuclear systems.

Eventually, to achieve the initial and extended topics mentioned earlier, we will broaden the Japan–Korea collaboration into a wider international platform.

Acknowledgments

This work was supported by National Research Foundation (NRF) grant (TOPTIER, RS-2024-00436392) by the Korea government of Ministry of Science and ICT (MSIT).