Background: Neutron-rich nucleus ^44S lies in the region where traditional N=28 shell closure weakens, leading to the emergence of shape coexistence and large-amplitude collective motion (LACM). Understanding the nature and degree of shape mixing in this nucleus remains an important and fascinating problem. Purpose: We investigate the manifestation of shape fluctuations in ^44S and examine how the electric transitions and the spectroscopic factors from one-neutron knockout reactions can serve as probes of shapes mixing. Method: The antisymmetrized molecular dynamics combined with the generator coordinate method (AMD+GCM) is used to study the structure of ^44S and ^43S. Calculations are performed by using Gogny effective interactions with two different parameter sets, D1S and D1M, to explore the interaction dependence of shape mixing. Monopole and quadrupole transition strengths and spectroscopic factors are evaluated. The cross sections for the ^44S(p,pn)^43S reaction are calculated within the distorted wave impulse approximation (DWIA). Results: The calculations reveal a strong interaction dependence of shape fluctuation in ^44S. The structural differences obtained from D1S and D1M interactions produce distinct patterns of the electric transitions, the spectroscopic factors, and the cross sections for ^44S(p,pn)^43S knockout reaction. Conclusion: The population of 3/2^- and 7/2^- states of ^43S is particularly sensitive to the underlying shape fluctuation in ^44S. Thus, the measurement of ^44S(p,pn)^43S reaction can provide a direct experimental probe.

The 1/2$^-$ resonant states in $^{13}{\rm C}$ are investigated to search for the Hoyle-analog state. In order to treat the resonance states located around the 3$\alpha+n$ threshold, the analytic continuation in the coupling constant (ACCC) has been combined with the real-time evolution method (REM). The properties of the 1/2$^-$ resonance states such as the radii and monopole transition probabilities are calculated. We show the 1/2$^-_3$ and 1/2$^-_4$ states are well-developed $\alpha$ cluster states, and the 1/2$^-_4$ state is a candidate of the Hoyle-analog state.

We present a method to determine the sign of quadrupole deformation (prolate or oblate) from low-energy α inelastic scattering. The sensitivity originates from the nuclear reorientation effect (RE), the self-coupling of excited states, which appears beyond the first-order distorted-wave Born approximation. Using a standard coupled-channel framework based on the macroscopic model, we demonstrate that RE modifies the interference pattern differently for β2 > 0 and β2 < 0. As a benchmark, we analyze α + 154Sm scattering at 50 MeV. The prolate solution reproduces the measured inelastic angular distribution, while the oblate solution fails to describe the forward-angle rise and the diffraction minima. A decomposition of the excitation mechanisms shows that the overall shape of the cross sections is governed by the nuclear RE, whereas Coulomb excitation mainly enhances the cross section at forward angles with little sensitivity to the sign. We conclude that low-energy α inelastic scattering provides a simple and broadly applicable tool to determine the sign of nuclear deformation.

Background: oblate-prolate shape coexistence in ^28Si has been discussed for decades, but the degree of shape mixing between these configurations remains poorly constrained. Purpose: We constrain the oblate-prolate mixing amplitudes in ^28Si using available experimental information and discuss the inter-band E0 transition strength. Methods: Oblate and prolate 0^+ and 2^+ configurations are obtained by antisymmetrized molecular dynamics combined with the generator coordinate method. Using these configurations as the basis states, we constrain the mixing amplitudes by simultaneously reproducing the measured charge radius, the quadrupole moment of the 2_1^+ state, and the in-band and inter-band B(E2) values. The strength of the density-dependent term in the Gogny interaction is also varied within a reasonable range. Results: In the ground state, the oblate component is dominant, and the prolate component in the ground state is limited to less than about 20%. For the 2_1^+ state, the allowed prolate component is smaller than that in the ground state. The present analysis does not tightly constrain the corresponding E0 transition strength, but an upper limit of ρ^2(E0;0_3^+→0_1^+) ≲ 0.206 is obtained. Conclusions: The low-lying 0^+ states of ^28Si may exhibit substantial oblate-prolate mixing. A measurement of the inter-band E0 transition strength would provide a quantitative determination of the mixing amplitude.

The disappearance of the N = 28 shell gap leads to enhanced quadrupole deformation and pronounced shape coexistence. In 44S, large shape fluctuations and several low-lying non-yrast states have been predicted. In this work, we demonstrate how spectroscopic factors can be used as a probe to investigate the ground-state configuration of 44S. Antisymmetrized molecular dynamics (AMD) combined with the generator coordinate method (GCM) is employed to calculate overlap amplitudes and spectroscopic factors and to examine the underlying configurations. The results show that the spectroscopic factors reflect the intrinsic shape of 44S and highlight their potential as a structural probe through knockout reactions.

Quartet correlations in neutron-rich Te isotopes are investigated within the quartet Bardeen-Cooper-Schrieffer (BCS) framework. Taking ^100Sn as an inert core, we consider two valence protons and valence neutrons occupying the 2d_5/2⊕1g_7/2 model space, and solve the quartet BCS variational equations with a charge-independent isovector pairing interaction. The effective pairing strength is constrained from empirical neutron pairing gaps in the Te isotopic chain. We find that the valence quartet number increases as the valence neutron number is enlarged from N_ val=2 to 14. The same increasing behavior is also found for the condensed quartet component. The proton occupation of the 1g_7/2 orbit is strongly enhanced relative to the conventional like-particle BCS reference and is driven close to the degeneracy-weighted limit. These results suggest that additional valence neutrons enhance the quartet admixture in the correlated quartet BCS state, while redistributing the fixed proton weight from pair-like configurations to quartet configurations.

We show that a two-proton emitter with a diproton-correlated initial state can act as a source of spin-correlated proton pairs. Using a time-dependent three-body model, we investigate the two-proton emission of ^16Ne (^14O+2p) and analyze the spin correlation of the emitted protons. We find that, when the emission proceeds as a democratic three-body process from an initial state containing a spin-singlet diproton correlation, the emitted protons exhibit a pronounced spin-correlation pattern exceeding the local-hidden-variable bound. This spin correlation closely resembles that of a pure spin-singlet pair. In contrast, this pattern is lost when the process is dominated by the sequential emission or when the initial diproton correlation is absent. These results demonstrate that a certain class of two-proton emitters can deliver spin-entangled proton pairs, and their spin correlation reflects the diproton correlation embedded in the initial state.

The ground state of ^12C has often been approximated by a mean-field picture. This conventional view has been challenged by recent nuclear theories suggesting non-negligible α-cluster formation, but experimental evidence remains inconclusive. Here, we show that existing ^12C(p,pα)^8Be data provide direct evidence for a pronounced α cluster formation in the ground state of ^12C. We analyze the data with distorted-wave impulse approximation using α preformation amplitudes from an unrestricted 3α cluster model and harmonic-oscillator-based models. The results show that the former reproduces the measured cross sections, whereas the latter underestimate them by more than an order of magnitude. Thus, contrary to conventional expectations, the data support a nearly fully developed three-α cluster structure in the ground state of ^12C.

For quantum meta-stable problems with three particles, the ^6Be and ^16Ne nuclei as two-proton (2p) emitters provide a testing field. Considering the complexity of many-body meta-stable systems, a tractable solver has been on demand. We apply the analytic continuation in coupling constant (ACCC) to these nuclei, and confirm that this method can solve such problems consistently to the time-dependent results as well as to the experimental data. The sensitivity of the 2p energies and widths to the proton-proton interaction is also investigated. The ^6Be shows a smooth shift from short-life to long-life systems according to the proton-proton interaction. Same is concluded for the 2^+ resonance of ^16Ne. In contrast, for the first and second 0^+ resonances of ^16Ne, their energies and widths show the avoid-crossing behaviour, due to the coupling of two configurations in the core-proton subsystem, ^15F. Since it requires only the bound-state solvers, the ACCC can be a low-cost option to solve three or more-body resonances.

We report accurate quantum simulations of medium-mass atomic nuclei -including oxygen, calcium, and nickel- on the RIKEN-Quantinuum Reimei trapped-ion quantum computer, achieving sub-percent accuracy. Using a symmetry-aware pair-unitary coupled-cluster doubles (pUCCD) ansatz implemented with a hard-core-boson mapping, and with particle-number-restoring post-selection, our ground-state energy estimates agree with noise-free statevector simulations and with exact diagonalization results on the order of 0.1

This review reports recent advancements in the study of cluster resonances using Antisymmetrized Molecular Dynamics (AMD). Cluster states, appearing as resonances above the particle-decay threshold, are crucial for understanding exotic cluster structures and reactions. A critical aspect of these studies is the calculation of the reduced width amplitude (RWA), which has been challenging due to the complexity of nucleon exchange between clusters. We introduce two novel methods for the computation of the RWA; the Laplace expansion and norm overlap methods. They have enabled more precise and computationally efficient calculations of RWA. We introduce their successful applications to key astrophysical nuclear reactions, such as ^12C+ ^12C and ^12C+ ^16O fusion processes, which play a vital role in stellar environments. Furthermore, we explore how these methods have advanced the study of exotic cluster structures, including the linear chain of α clusters and the ^6He cluster in light nuclei.

We systematically investigate the size evolution of the di-neutron (2n), di-proton (2p), and deuteron (d) in 6He, 14Be, 17B, 6Be, 17Ne, and 6Li using microscopic calculations. Remarkably, all nucleon pairs exhibit a universal size compression at the nuclear surface, regardless of their species and binding energies. These features correspond to the BCS- and BEC-like nucleon pairs, which recent experimental techniques can further investigate.

We confirm by using the Skyrme Hartree-Fock-Bogoliubov calculation that ^164Pb is a possible heaviest N = Z doubly magic nucleus whose lifetime is long enough to be measured on accelerator experiments. We estimate the proton-emission and alpha-decay half-lives of ^164Pb. The estimated proton-emission half-life ranges from 0.1 ps to 10 ns, while the alpha decay can be safely neglected.

The overlap function and the spectroscopic factor (SF) of alpha-cluster and valence neutron in 12Be are calculated by the generator coordinates method (GCM) with the cluster model. By fixing the distance between the alpha- clusters' generated coordinates, we make a theoretical experiment to analyze the relationship between the alpha- clustering separation and the orbital occupation of the valence neutron in 12Be. The analysis of the results shows that the percentage of the sigma-orbital occupation in 12Be is positively related to the clustering separation.

We simulate ultra-central collisions of prolate uranium-uranium nuclei at intermediate energies using the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to investigate the impact of momentum anisotropy on spatial geometric effects. By defining the quadrupole deformation parameter in momentum space β_p, we establish an ellipsoidal Fermi surface, aligning its rotational symmetry axis with the one in coordinate space. It is found that oblate momentum density enhances elliptic flow v_2, while prolate momentum density has the opposite effect, particularly pronounced in the outer, high transverse momentum p_t region. Momentum anisotropy also causes differences in the initial momentum mean projection along the beam direction, with larger projections producing more pion mesons. Additionally, significant effects on mean square elliptic flow are observed in non-polarized collisions. We further examine the relationship between the v_2-p_t slope and β_p, eliminating systematic errors through the two-system ratio. These findings provide important references for experimentalists in heavy-ion collisions and valuable feedback to theorists regarding nuclear structure.

The ^16Ne nucleus is a two-proton (2p) emitter, where an interference of two resonances is expected since its core-proton subsystem, ^15F=^14O+p, has separate resonances in the s_1/2 and d_5/2 channels. We theoretically investigate the 2p emission from the unbound 0^+ state of ^16Ne. To investigate the 2p-emitting process, we perform the time-dependent calculations based on the three-body model of ^14O+p+p. By evaluating the survival probability, a deviation from the exponential decay is obtained. In correspondence, the 2p-energy spectrum of ^16Ne is not of the single resonance, but an interference of the main narrow and the second broad resonances is obtained. In time-dependent calculations, the sequential 1p-1p emission from ^16Ne is relatively dominant as long as the manifest s_1/2 resonance in ^15F exists. The diproton-correlating emission becomes active only if the s_1/2 resonance is broad. As conclusion, the 2p emission of ^16Ne is one example of the multi-resonance interference in open-quantum systems. The s_1/2 intermediate resonance is essential to realize this interference, and induces the sequential emission. The 2p-decaying state is predicted to have the spin-singlet entanglement independently of whether the emission is sequential or correlating.

The reduced width amplitudes (RWA) and the spectroscopic factor (S-factor) of α-cluster and valence neutron in ^12Be are calculated by the generator coordinates method (GCM) with the cluster model. By fixing the distance between the α-clusters' generated coordinates, we make a theoretical experiment to analyze the relationship between the α-clustering separation and the orbital occupation of the valence neutron in ^12Be. The analysis of the results shows that the percentage of the σ orbital occupation in ^12Be is positively related to the clustering separation.

We have examined the hypothesis by Bijker and Iachello who asserted that ^12C has an internal structure with three α particles arranged in a triangular shape, leading to the formation of the ground rotational band consisting of 0^+ , 2^+ , 3^- , 4^± and 5^- states. Following this idea, we reconstructed the intrinsic shape of ^12C using experimental electron scattering data with minimal theoretical assumption. Our sole assumption was that the observed 0^+_1 , 2^+_1 , 3^-_1 , and 4^+_2 states share a common internal structure, forming a rotational spectrum. The reconstructed intrinsic density showed a beautiful triangular shape with three peaks implying α cluster formation in the ground band.