I shall present a very brief summary of subjects selected from what Prof. Akito Arima has done in the past years. I will focus on the initial works on the configuration mixing and on the Interacting Boson Model. Since there are many literatures on these subjects, I shall concentrate what have been done at the initial or at the pre-history stages. By doing this, we shall see how Prof. Akito Arima started from the scratch.

The shell model of atomic nuclei has been in intensive use since the middle of the previous century. This simple model of very complex nuclei, offers a quantitative description of its many features. Other features follow from small deviations from the extreme picture. Our friend and colleague Akito Arima made seminal contributions to this field starting with his famous paper with Horie on the magnetic moments of nuclei [Prog. Theor. Phys. 11, 509 (1954)]. In the following, a detailed description of a simple example is considered. It is the 1f_7/2 shell of the neutrons in the nuclei between ⁴⁰Ca and ⁴⁸Ca and of the protons in the nuclei between ⁴⁸Ca and ⁵⁶Ni. The results demonstrate the power and elegance of the shell model. They show how simplicity arises out of complexity. It is also shown how small deviations from the simple shell model lead to effects, in which valence neutrons act as if they carry electric charge.

Nuclei are complex objects yet display remarkable simplicities and regular patterns. The study of these and their origins has long been one of the twin pillars of nuclear structure research. We will discuss the behavior of atomic nuclei from this point of view. A key element will be the advantages of looking at the same data from different perspectives and of inter-relating these perspectives.

After briefly reviewing the theoretical concepts and numerical methods in lattice QCD, recent simulation results of the hadron masses and hadron interactions with nearly physical quark masses are presented. Special emphasis is placed on the baryon-baryon interactions on the basis of the HAL QCD method where the integro-differential equation for the equal-time Nambu–Bethe–Salpeter amplitude plays a key role to bridge a gap between the multi-baryon correlation and the scattering observable such as the phase shift.

We review our calculation method, Gaussian expansion method (GEM), to solve accurately the Schrödinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. GEM was proposed 30 years ago and has been applied to a variety of subjects in few-body (3- to 5-body) systems, such as 1) few-nucleon systems, 2) few-body structure of hypernuclei, 3) clustering structure of light nuclei and unstable nuclei, 4) exotic atoms/molecules, 5) cold atoms, 6) nuclear astrophysics and 7) structure of exotic hadrons. Showing examples in our published papers, we explain i) high accuracy of GEM calculations and its reason, ii) wide applicability of GEM to various few-body systems, iii) successful predictions by GEM calculations before measurements. The total bound-state wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for shortrange and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution than in the case of real-range Gaussians, especially, when the wave function has many nodes (oscillations). These basis functions can well be applied to calculations using the complex-scaling method for resonances. For the few-body scattering states, the amplitude of the interaction region is expanded in terms of those few-body Gaussian basis functions.

This contribution reviews the symmetry properties of the interacting boson model of Arima and Iachello. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of partial dynamical symmetry and quasi dynamical symmetry, which can be beautifully illustrated in the context of the interacting boson model. The main conclusion of the analysis is that dynamical symmetries are scarce while their partial and quasi extensions are ubiquitous.

We discuss cluster phenomena in light nuclei. As examples of typical cluster structures, we first review cluster structures of ¹²C, ¹⁶O, and ²⁰Ne, and then introduce some topics of cluster phenomena in light neutron-rich nuclei such as Be and C isotopes. A particular attention is paid on coexistence of cluster and shell-model aspects.

Nuclear magnetic moment is an important physical variable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be successful in describing the nuclear ground-states and excited states properties. However, a long-standing problem is its failure to predict magnetic moments. This article reviews the recent progress in the description of the nuclear magnetic moments within the covariant density functional theory. In particular, the magnetic moments of spherical odd-Anuclei with doubly closed shell core plus or minus one nucleon and deformed odd-Anuclei.

The study of cluster structures in light nuclei is extending to the heavy nuclei in these years. As for the stable N = Z nuclei, from the lighter ⁸Be, ¹²C nuclei to the heavier ²⁰Ne and even the ⁴⁰Ca and ⁴⁴Ti medium nuclei, the α cluster structures have been well studied and confirmed. In heavy nuclei, due to the dominated mean field, the existence of α cluster structure is not clear as light nuclei but some clues were found for indicating the core+α cluster structure in some nuclei, in particular, the ²⁰⁸Pb+α structure in ²¹²Po. We review some recent progress about the theoretical and experimental explorations of the α-clustering effects in heavy nuclei. We also discuss the possible α cluster structure of heavy nuclei from the view of α decay.

Research activities of nuclear physics at Radioactive Isotope Beam Factory over 10 years are reviewed and future directions are also discussed. Conceptual ideas in designing the facility as well as experimental devices are introduced. Special emphasis is given to highlighted results obtained at RIBF.

In recent years, extensive short-lived nuclear mass measurements have been carried out at the Heavy- Ion Research Facility (HIRFL) in Lanzhou using Isochronous Mass Spectrometry (IMS). The obtained mass values have been successfully applied to nuclear structure and astrophysics studies. In this contribution, we give a brief introduction to the nuclear mass measurements at HIRFL-CSR facility. Main technical developments are described and recent results are summarized. Furthermore, we envision the future perspective for the next-generation storage ring facility HIAF in Huizhou.

The main progresses in the multinucleon transfer reactions at energies close to the Coulomb barrier are reviewed. After a short presentation of the experimental progress and theoretical progress, the predicted production cross sections for unknown neutron-rich heavy nuclei and the trans-uranium nuclei are presented.

Atomic nuclei are complex systems with gigantic configuration spaces, therefore truncations of model spaces are indispensable. Due to the short-range nature of the nuclear interactions, one may resort to a truncation by using coherent nucleon-pairs which are conveniently further simplified as bosons, such as sd bosons. The discovery of the spin-zero ground state dominance with random two-body interactions led to a series of studies on regular structure for sd bosons in the presence of random interactions, and this review article summarizes studies along this line in last two decades. We concentrate on various patterns exhibited in sd boson systems, and demonstrate that many random samples which were thought to be noisy exhibit very regular patterns, some of which are interpreted in terms of the U(5), O(6), \overline{\mathrm{O}\left(6\right)}, SU(3), and \overline{\mathrm{S}\mathrm{U}\left(3\right)} dynamical symmetries of the sd interacting boson model.