arXiv subjects

Takayuki Myo

Publications and source records attributed to Takayuki Myo.

At least 19 recordsLinked to original sources

arXiv2026

Physics of many-body resonances with complex scaling and applications to light unstable nuclei

We review the exotic phenomena in light unstable nuclei with a focus on many-body resonances, which can decay into more than two constituents, and are frequently observed in unstable nuclei above the three-body threshold energy. The complex scaling transformation of the Schrödinger equation is a powerful method for describing many-body resonances, because it separates the continuum spectra into resonant and non-resonant continuum ones. Since the asymptotic wave functions of the resonances are regularized in the complex scaling, many-body resonances are described using the $L^2$ basis functions in the eigenvalue problem. The properties of many-body resonances can then be discussed in the same way as those of the bound states. We apply the complex scaling to the system consisting of a stable nucleus and valence nucleons and investigate many-body resonances in neutron-rich and proton-rich light nuclei. Using the eigenstates obtained with the complex scaling, we construct the extended completeness relation and the Green's function. They are used to calculate the level densities and the general transition strengths into many-body unbound states. We also discuss the interpretation of the complex expectation values associated with resonances, which remains an open problem. We propose a possible scheme for it in terms of the complex-scaled Green's function.

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arXiv2026

Examination of the $α$-cluster breaking in the four $0^+$ bands of $^{12}$C with the variation of multiple bases of the antisymmetrized molecular dynamics

I investigate $^{12}$C, particularly the four kinds of the $0^+$ bands with various types of the $3α$ configurations. These states are obtained in the variation of the multiple bases of the antisymmetrized molecular dynamics, where the bases are optimized simultaneously in the variation of the total energy. In the $0^+_2$ Hoyle state and the $0^+_3$ linear-chain state, I confirm a mixture of the $α$-cluster breaking of the $s$-wave configuration with contributions from the spin-orbit force, while the $0^+_4$ state exhibits a relatively pure $3α$ cluster state characterized by a large radius. The $2^+_{2-4}$ and $4^+_{2-4}$ states also tend to be the pure $3α$ cluster states. The monopole transitions between the $0^+_{2}$ and $0^+_{4}$ bands exhibit large values, suggesting breathing mode of the $3α$ states in the $0^+_4$ band. This conclusion aligns with the predictions of the $3α$ models with an $α$ condensate and also with a neural network, although the order of the $0^+_3$ and $0^+_4$ bands is reversed in the present results due to the attraction of the spin-orbit force.

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arXiv2026

Time evolution formalism in the complex scaling method: Application to the E1 response of $^6$He

Background: The complex scaling method (CSM) has been successfully used to describe many-body resonances as eigenvalues of the complex-scaled Hamiltonian in an appropriate $L^2$ basis representation. Its scope has subsequently been extended to many-body continuum states, strength functions, and scattering observables. However, a general framework that incorporates time evolution within the same CSM framework has not yet been established. Purpose: We formulate a time-evolution formalism as a natural extension of the CSM based on the extended completeness relation (ECR), and apply it to the electric dipole (E1) excitation of $^6$He in order to clarify how an initially correlated three-body configuration evolves into continuum states. Methods: Time evolution is described by a complex-scaled time-evolution operator represented with the ECR. The formalism is first tested in a simple two-body model through comparison with a direct numerical solution of the time-dependent Schrödinger equation. It is then applied to the E1 excitation of $^6$He in an $α+ n + n$ three-body model, and the density distributions are analyzed in different Jacobi coordinate systems. Results: The present formalism reproduces the wave-packet evolution obtained in the direct time-dependent calculation. In the application to $^6$He, the initial E1-excited state exhibits a correlated configuration and evolves into spatially extended continuum states. The time evolution of the density distributions indicates the coexistence of sequential decay through a core-neutron subsystem and direct breakup. Conclusions: The present formalism extends the scope of the CSM from spectral and scattering observables to real-time continuum dynamics, and provides a unified framework that connects initial-state correlations, continuum structure, and decay dynamics in weakly bound nuclei.

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arXiv2026

Cluster-breaking and reconfiguration effects in $_Λ^{12}\rm{B}$ hypernucleus

We investigate the cluster-breaking effect and spatial distribution of negative-parity states in the $_Λ^{12}\rm{B}$ hypernucleus using the Hyper-Brink model with cluster-breaking(CB-Hyper-Brink) optimized via Control Neural Network (Ctrl.NN). The results demonstrate that the inclusion of cluster-breaking is essential for accurately reproducing the observed low-lying energy levels and for making reliable predictions of the Hoyle-analog state 1-4 in $_Λ^{12}\rm{B}$. Cluster-breaking manifests as strong spin-orbit correlations and the dissolution of ideal cluster configurations, as revealed by the analysis of one-body spin-orbit operator expectation values and the spatial overlap with projected cluster bases. The interplay between short-range repulsion and intermediate-range attraction in the Lambda N interaction induces the cluster reconfiguration effect, which is characterized by the coexistence of Lambda-alpha and Lambda-triton correlations; this reconfiguration effect leads to a modest stabilization and shrinkage of cluster structures. The variation in electric quadrupole transition strengths, B(E2), between the ground and Hoyle-analog states serves as a sensitive probe for the degree of cluster-breaking, providing direct evidence for its physical relevance. These findings highlight the crucial role of cluster-breaking in characterizing the hypernuclear structure and offer a comprehensive framework for understanding the interplay between clustering and shell-model dynamics in hypernuclei.

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arXiv2026

Quadrupole transitions of $^{10}$C and their isospin symmetry with $^{10}$Be

We investigate the structures of $^{10}$C focusing on the quadrupole properties in comparison with the mirror nucleus $^{10}$Be. We describe $^{10}$C and $^{10}$Be in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD), in which the multiple AMD bases are optimized simultaneously in the total-energy variation. In the monopole transitions, we confirm the isospin symmetry between $^{10}$C and $^{10}$Be by exchanging protons and neutrons. In the quadrupole transitions, most cases show larger values in $^{10}$C than those of $^{10}$Be, except for the transition of $2^+_1\to 0^+_1$. The transition of $2^+_1\to 0^+_1$ shows similar values in the two nuclei in spite of the different proton numbers, which agrees with the experimental situation as an anomaly. This relation comes from the small proton deformation in $^{10}$C due to its subclosed nature and the large proton deformation in $^{10}$Be due to two-$α$ clustering. This property can also be seen in the quadrupole moments of the two nuclei. In the neutron deformations of $^{10}$C and $^{10}$Be, the opposite tendency of protons is confirmed and these results ensure the isospin symmetry between the two nuclei. We also confirm the large quadrupole transitions between the elongated linear-chain states. It would be desirable for future experiments to investigate the present characteristics of the transitions in the two nuclei.

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arXiv2026

Shell and cluster structures in $^{20}$Ne in the variation of multiple bases of the antisymmetrized molecular dynamics

We investigate the structures of $^{20}$Ne in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD). In this method, the multiple AMD bases are superposed and optimized simultaneously in the total-energy variation. This scheme is beneficial for describing the various configurations in $^{20}$Ne. In the results, we confirm the shell and cluster structures in the $K^π=0^+_{1-4}$ bands, such as the deformed states in the $K^π=0^+_{1,4}$ bands with the $α$ cluster development, and the spherical shell-like states in the $K^π=0^+_2$ band, the latter of which is difficult to describe in the previous AMD calculations imposing the quadrupole deformation. We evaluate the monopole and quadrupole transitions in these states. The negative parity states of $^{20}$Ne with $K^π=0^-$ and $2^-$ are discussed in relation to the shell and cluster structures. As a result, six kinds of the $K^π$ bands in $^{20}$Ne are described comprehensively in the microscopic framework of nuclei.

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arXiv2025

Hypernuclear cluster states of $_Λ^{12}\rm{B}$ Unveiled through Neural Network-Driven Microscopic Calculation

We investigate the hypernuclear cluster states of $_Λ^{12}\mathrm{B}$ using a neural-network-driven microscopic model. We extend the Control Neural Networks (Ctrl.NN) method and systematically calculate the positive-parity spectrum of $_Λ^{12}\mathrm{B}$. By incorporating $sd$-shell excitations and parity-coupling effects into the $_Λ^{12}\mathrm{B}$ hypernuclear system, we reveal structural changes, including clustering effects and new configurations such as isosceles-triangle and $α$-$t$-$α$ linear-chain structures. Furthermore, by comparing with experimental data, we identify that many peaks ($\#$6 and $\#$8) can be interpreted as $p_Λ$ dominant states, which is consistent with shell-model predictions. Notably, based on our analysis of the excited states of $_Λ^{12}\mathrm{B}$, we propose possible candidates for previously unexplained or controversial experimental peaks.

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arXiv2025

Cluster configurations in Li isotopes in the variation of multi-bases of the antisymmetrized molecular dynamics

We investigate the cluster configurations in Li isotopes, which are described in the optimization of the multi-Slater determinants of the antisymmetrized molecular dynamics. Each Slater determinant in the superposition is determined simultaneously in the variation of the total energy. The configurations of the excited states are obtained by imposing the orthogonal condition to the ground-state configurations. In Li isotopes, various cluster configurations are confirmed and are related to the thresholds of the corresponding cluster emissions. For $^5$Li, we predict the $^3$He+$d$ clustering in the excited state as well as the mirror state of $^5$He with $^3$H+$d$. For $^{6-9}$Li, various combinations of the clusters are obtained in the ground and excited states, and the superposition of these basis states reproduces the observed energy spectra. For $^9$Li, we predict the linear-chain states consisting of various cluster configurations at 10--13 MeV of the excitation energy.

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arXiv2024

Neutron skin thickness for $^{208}$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for $^{48}$Ca, O, N, C isotopes from reaction and interaction cross sections

Foster {\it et al.} measured total neutron cross sections $σ_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Carlson {\it et al.} measured $σ_{\rm R}$ for $p$+$^{48}$Ca scattering in $23 \text{--} 48$MeV. Tanaka {\it et al.} measured $σ_{\rm I}$ for $^{42\text{--}51}$Ca + $^{12}$C scattering at 280MeV/u. Bagchi {\it et al.} measured the charge-changing (CC) cross sections and determined proton radii $r_{\rm p}({\rm CC})$ for $^{14,15,17 \text{--} 22}$N from the CC cross sections. Kanungo {\it et al.} measured the CC cross sections and extracted $r_{\rm p}({\rm CC})$ for $^{12\text{--} 19}$C. Kaur {\it et al.} measured the CC cross sections and determined $r_{\rm p}({\rm CC})$ for $^{16,18 \text{--} 24}$O. Our 1st aim is to extract $r_{\rm skin}^{208}$ from the the $σ_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Our 2nd aim is to determine $r_{\rm skin}^{48}({\rm skin})$ from $σ_{\rm R}$ on p+$^{48}$Ca scattering in $E_{\rm lab}=23 \text{--} 48$MeV. Our 3rd aim is to find light stable nuclei having nuclei having large $r_{\rm skin}$. We use the Kyushu $g$-matrix folding model for lower $E_{\rm lab}$ and the folding model based on the Love-Franey $t$-matrix for higher $E_{\rm lab}$. We determine $r_{\rm skin}^{48}({\rm skin})=0.163 \pm 0.037{\rm fm}$ from the $σ_{\rm R}$ on p+$^{48}$Ca scattering, using the Kyushu $g$-matrix folding model with the D1M-GHFB+AMP proton and neutron densities. We show that D1M-GHFB+AMP is better than D1S-GHFB+AMP for the matter radius and the binding energy. Our skin value is consistent with $r_{\rm skin}^{48}({\rm CREX})$. For C, N, O isotopes, we find that $r_{\rm skin}= 0.267 \pm 0.056$~fm for $^{14}$N and $r_{\rm skin}= 0.197 \pm 0.067$~fm for $^{17}$O. Our value $r_{\rm skin}^{208}=0.309 \pm 0.057$fm agrees with $r_{\rm skin}^{208}({\rm PREX2})$.

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arXiv2024

Evidence for Three-$α$ Breathing Modes Uncovered by Control Neural Network

This work introduces a new Control Neural Network (Ctrl.NN) method to uncover evidence of exotic quantum state, \textit{i.e.}, the breathing modes in 3-$α$ resonant states of $^{12}$C nucleus. We provide the most precise microscopic description to date for the $^{12}$C energy spectrum, identify two new exotic breathing states, and uncover strong evidence that directly connects the recent experimental observations to the breathing modes. The Ctrl.NN method significantly simplifies numerical calculations of quantum systems under multiple constraints and offers a new perspective for solving the nuclear many-body problem.

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arXiv2024

Generalized coherent states satisfying the Pauli principle in a nuclear cluster model

We propose a new basis state, which satisfies the Pauli principle in the nuclear cluster model. The basis state is defined as the generalized coherent state of the harmonic oscillator wave function using a pair of the creation operators and is orthogonal to the Pauli-forbidden states having smaller quanta. In the coherent basis state, the range parameter is changeable and controls the radial dilation. This property is utilized for the precise description of the relative motion between nuclear clusters. We show the reliability of this framework for the $2α$ system of $^8$Be in the semi-microscopic orthogonality condition model. We obtain the resonances and non-resonant continuum states of $2α$ with complex scaling. The resonance solutions and the phase shifts of the $α$-$α$ scattering agree with those using the conventional projection operator method to remove the Pauli-forbidden states. We further discuss the extension of the present framework to the multi-$α$ cluster systems using the SU(3) wave functions.

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arXiv2023

Variation of multi-Slater determinants in antisymmetrized molecular dynamics and its application to $^{10}$Be with various clustering

We propose a method to optimize the multi-Slater determinants of the antisymmetrized molecular dynamics (AMD) in the linear combination form and apply it to the neutron-rich $^{10}$Be nucleus. The individual Slater determinants and their weights in the superposition are determined simultaneously according to the variational principle of the energy of the total wave function. The multi-AMD basis states of $^{10}$Be show various cluster structures as well as the shell-model type. In the cluster configurations, different intercluster distances are superposed automatically indicating the role of the generator coordinates. We further introduce a procedure to obtain the configurations for the excited states imposing the orthogonal condition to the ground-state configurations. In the excited states of $^{10}$Be, the linear-chain-like structure is confirmed consisting of various clusters. The energy spectrum using the obtained basis states reproduces the experiments. The present framework can be the method to find the optimal multi-configuration for nuclear ground and excited states.

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arXiv2023

Resonances and scattering in microscopic cluster models with the complex-scaled generator coordinate method

The generator coordinate method of a microscopic cluster model is developed to treat the resonance and scattering of nuclear clusters with complex scaling. We consistently derive the formulation of the complex scaling for the microscopic cluster model, in which only the relative motions between clusters are transformed in the generator coordinate wave function. We also reveal the applicability of this method to the cluster wave function. Furthermore, we demonstrate this framework in the 2$α$ system of $^8$Be and obtain the solutions of resonance and non-resonant continuum states. Using these solutions, we calculate the level density, which brings the phase shifts of the cluster-cluster scattering. This work becomes the foundation in the description of the multi-cluster scattering states of nuclei in a microscopic framework with complex scaling.

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arXiv2023

Structure of neutron-rich He $Λ$ hypernuclei using the cluster orbital shell model

We calculated the energy spectra of the neutron-rich He $Λ$ hypernuclei with $A=6$ to 9 within the framework of an $α+ Λ+Xn$ ($X=1$--4) cluster model using the cluster orbital shell model. The employed constituent particles reproduce their observed properties. For resonant states of core nuclei such as $^5$He, $^6$He, and $^7$He, the complex scaling method is employed to obtain energies and decay widths. The calculated ground states of $^6_Λ$He and $^7_Λ$He are in good agreement with published data. The energy levels of $^8_Λ$He and $^9_Λ$He are predicted. In $^9_Λ$He, we find one deeply bound state and two excited resonant states, which are proposed to be produced at the Japan proton accelerator research complex (J-PARC) by the double-charge-exchange reaction $(π^-, K^+)$ using a $^9$Be target.

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arXiv2023

Soft dipole resonance in $^8$C and its isospin symmetry with $^8$He

We investigate the soft dipole resonance in the proton-rich nucleus $^8_6$C$_2$, which is a collective dipole oscillation of four valence protons against the $α$ core,and discuss the isospin symmetry with the mirror nucleus $^8_2$He$_6$. We use the $α+N+N+N+N$ five-body cluster model and many-body resonances are obtained using the complex-scaling method. The $1^-$ resonance of $^8_6$C$_2$ is confirmed at the excitation energy of 13 MeV with a large decay width of 24 MeV, and its structure is similar to the soft dipole resonance in $^8_2$He$_6$, such as the configuration mixing and the spatial properties. These results indicate a good isospin symmetry in the soft dipole resonances of two nuclei with a common collective excitation of multiproton and multineutron, while the ground states of two nuclei show different properties due to the Coulomb repulsion of valence protons in $^8_6$C$_2$, leading to the symmetry breaking. In conclusion, the appearance of the isospin symmetry differs depending on the states of $^8_6$C$_2$ and $^8_2$He$_6$.

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arXiv2023

Possible interpretation of the complex expectation values associated with resonances

We propose a possible scheme to interpret the complex expectation values associated with resonances having the complex eigenenergies. Using the Green's function for resonances, the expectation value is basically described by the Breit-Wigner distribution as a function of the real excitation energy. In the expression of the complex expectation values for resonances, the real part brings the integral value of the distribution, while the imaginary part produces the deviation from the Breit-Wigner distribution,which explains a shift of the peak in the strength from the resonance energy. We apply the present scheme to the several nuclear resonances of $^{12}$C including the Hoyle state, and neutron/proton-rich nuclei of $^6$He, $^6$Be, $^8$He, and $^8$C. In these nuclei, many-body resonances are obtained as the complex-energy eigenstates under the correct boundary condition using the complex scaling method, and their nuclear radii are uniquely evaluated. We discuss the peculiar energy dependence of the strength function of the square radius for the resonances in these nuclei.

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arXiv2022

Successive variational approach with the tensor-optimized antisymmetrized molecular dynamics for the $^5$He nucleus

We study $^5$He variationally as the first $p$-shell nucleus in the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon--nucleon interaction without any renormalization. In TOAMD, the central and tensor correlation operators promote the AMD's Gaussian wave function to a sophisticated many-body state including the short-range and tensor correlations with high-momentum nucleon pairs. We develop a successive approach by applying these operators successively with up to double correlation operators to get converging results. We obtain satisfactory results for $^5$He, not only for the ground state but also for the excited state, and discuss explicitly the correlated Hamiltonian components in each state. We also show the importance of the independent optimization of the correlation functions in the variation of the total energy beyond the condition assuming common correlation forms used in the Jastrow approach.

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arXiv2022

Soft dipole resonance in neutron-rich $^8$He

In neutron-rich $^8$He, we study the soft dipole resonance, which is regarded as a dipole oscillation of four valence neutrons against the $^4$He core, and its effect on the low-energy electric dipole strength with a $^4$He+$n$+$n$+$n$+$n$ five-body cluster model. This work is an extended study of an earlier letter [T. Myo and K. Katō, Phys. Rev. C106, L021302 (2022)]. The five-body unbound $1^-$ states of $^8$He are obtained with the complex energy eigenvalues by using the complex scaling method and the dipole strength is calculated in terms of the complex-scaled Green's function. Two kinds of the dominant excitation modes are confirmed in the dipole strength below 20 MeV of the excitation energy. The strengths below 10 MeV are exhausted by the $^7$He+$n$ channel, which sequentially decays to $^6$He+$n$+$n$. Above 10 MeV, the strengths arise from the soft dipole mode of four neutrons ($4n$) oscillating against the $^4$He core. We further explore the possibility of the soft dipole resonance for this state by carefully searching for the resonance pole and finally predict the corresponding resonance with the excitation energy of 14 MeV and the decay width of 21 MeV. The soft dipole resonance exhausts about half of the dipole strength in the relative motion between the $^4$He core and $4n$.

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