arXiv subjects

Hiroshi Toki

Publications and source records attributed to Hiroshi Toki.

At least 19 recordsLinked to original sources

arXiv2026

Exploring Pion-Induced High-Momentum Components in Nuclei via $(p,p'\pi)$ Reactions

Pion exchange plays a fundamental role in nuclear structure and is responsible for tensor correlations and high-momentum components in nuclei. The $(p,p'\pi)$ reaction provides a unique opportunity to investigate pion dynamics under large-momentum-transfer conditions. Its three-body kinematics allows large momentum transfer to be achieved while keeping the excitation energy of the residual nucleus low. We investigate the kinematical properties of the $^{12}\mathrm{C}(p,p'\pi^+)^{12}\mathrm{B}$ reaction using Lorentz-invariant three-body phase-space calculations. The calculations were performed for a 392-MeV proton beam assuming a constant transition amplitude. The resulting momentum-transfer map and phase-space distribution identify experimentally accessible regions of large momentum transfer and provide guidance for optimizing a double-arm spectrometer experiment at RCNP. The present study establishes a model-independent kinematical foundation for future investigations of pion-induced correlations, high-momentum components, and pion dynamics in nuclei.

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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-$\alpha$ 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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arXiv2025

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

We investigate the cluster-breaking effect and spatial distribution of negative-parity states in the $_\Lambda^{12}\rm{B}$ 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 $_\Lambda^{12}\rm{B}$. 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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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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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

Finite particle-number description of symmetric nuclear matter with spin excitations of high-momentum pairs induced by tensor force

We study the symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spin of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighbouring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at the normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.

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arXiv2022

New many-body method using cluster expansion diagrams with tensor-optimized antisymmetrized molecular dynamics

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central-types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provides the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.

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arXiv2021

Role of unitary correlation operator on high-momentum antisymmetrized molecular dynamics using bare NN interaction for 3H and 4He

We extend the high-momentum antisymmetrized molecular dynamics (HMAMD) by incorporating the short-range part of the unitary correlation operator method (UCOM) as the variational method of finite nuclei. In this HMAMD+UCOM calculation of light nuclei, the HMAMD is mainly in charge of the tensor correlation with up to the four-body correlation, while the short-range correlation is further improved by using the UCOM. The binding energies of the 3H and 4He nuclei are calculated with this HMAMD+UCOM using the AV8' bare nucleon-nucleon (NN) interaction. The different roles of the short-range and tensor correlations from the HMAMD and UCOM are analyzed in the numerical results. Compared with the previous calculations based on the different variational methods, this newly extended HMAMD+UCOM method can almost provide the consistent results with the ab initio results.

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arXiv2020

Finite particle number description of neutron matter using the unitary correlation operator and high-momentum pair methods

By using bare Argonne V4' (AV4'), V6' (AV6'), and V8' (AV8') nucleon-nucleon (NN) interactions respectively, the nuclear equations of state (EOSs) for neutron matter are calculated with the unitary correlation operator and high-momentum pair methods. The neutron matter is described under a finite particle number approach with magic number $N=66$ under a periodic boundary condition. The central short-range correlation coming from the short-range repulsion in the NN interaction is treated by the unitary correlation operator method (UCOM) and the tensor correlation and spin-orbit effects are described by the two-particle two-hole (2p2h) excitations of nucleon pairs, in which the two nucleons with a large relative momentum are regarded as a high-momentum pair (HM). With the 2p2h configurations increasing, the total energy per particle of neutron matter is well converged under this UCOM+HM framework. By comparing the results calculated with AV4', AV6', and AV8' NN interactions, the effects of the short-range correlation, the tensor correlation, and the spin-orbit coupling on the density dependence of the total energy per particle of neutron matter are demonstrated. Moreover, the contribution of each Hamiltonian component to the total energy per particle is discussed. The EOSs of neutron matter calculated within the present UCOM+HM framework agree with the calculations of six different microscopic many-body theories, especially in agreement with the auxiliary field diffusion Monte Carlo calculations.

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arXiv2020

Evolution of clustering structure through the momentum distributions in $^{8-10}$Be isotopes

We investigate the evolution of clustering structure through the momentum distributions in the $^{8-10}$Be isotopes. The nucleon dynamics within the inter-cluster antisymmetrization are discussed via the momentum distribution of a Brink type $α$-$α$ wave function. For the state with a small $α$-$α$ distance, we observe a significant depression with a dip structure at zero-momentum and an enhanced tail at relatively higher momentum region. In addition, we find the "cluster structure" in the intrinsic frame of momentum space, which is complementary to its significant $α$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8-10}$Be isotopes, the Tohsaki-Horiuchi-Schuck-R{ö}pke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at the zero-momentum of nucleon distribution for the two $α$-clusters within $^{8-10}$Be isotopes. For the compact $^{10}$Be nucleus, the momentum distribution of all nucleons shows significant depression at zero-momentum with a dip structure, which is found to be contributed by both the inter-cluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $α$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

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arXiv2020

High-momentum components in the $^4$He nucleus caused by inter-nucleon correlations

High-momentum components of nuclei are essential for understanding the underlying inter-nucleon correlations in nuclei. We perform the comprehensive analysis for the origin of the high-momentum components of $^4$He in the framework of Tensor-optimized High-momentum Antisymmetrized Molecular Dynamics (TO-HMAMD), which is a completely variational approach as an $ab$ $initio$ theory starting from the bare nucleon-nucleon ($NN$) interaction. The analytical derivations are provided for the nucleon momentum distribution of the Antisymmetrized Momentum Dynamics (AMD) wave functions, with subtraction of center-of-mass motion. The nucleon momentum distribution for $^4$He is calculated by applying a new expansion technique to our $ab$ $initio$ wave function, and agrees with the values extracted from experimental data up to the high-momentum region. Fine-grained analysis is performed for the high-momentum components in $^4$He with respect to different nucleon correlations. Contributions from tensor, central with short-range, and many-body correlations are extracted from the nucleon momentum distributions. The manifestation of tensor correlation around 2 fm$^{-1}$ region is explicitly confirmed by comparing the momentum distributions predicted using different types of $NN$ interactions with and without the tensor force.

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arXiv2020

The one-pion-exchange potential with contact terms from lattice QCD simulations

The pion-mass-dependent nucleon-nucleon ($NN$) potentials in term of one-pion exchange and contact terms are obtained from the latest lattice QCD simulations of two-nucleon system, which employ the forms of leading order (LO) $NN$ potential from the chiral effective field theory and thus are named as the LO chiral potential in this work. We extract the coefficients of contact terms and cut-off momenta in these potentials, for the first time, by fitting the phase shifts of $^1S_0$ and $^3S_1$ channels generated by the results of HALQCD collaboration with various pion masses from $468.6$ MeV to $1170.9$ MeV. The low-energy constants in the $^1S_0$ and $^3S_1$ channels become weaker and approach each other for larger pion masses. These LO chiral potentials are applied to symmetric nuclear and pure neutron matter within the Brueckner-Hartree-Fock method. At this moment, however, we do not have yet the information of the $P$-wave $NN$ interaction to be provided by the lattice QCD simulations for full description of nuclear matter. Our results will enhance the development of nuclear structure and nuclear matter by controlling the contribution of the pionic effect and illuminate the role of chiral symmetry of the strong interaction in complex system.

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arXiv2019

Variational calculation of nuclear matter in finite particle number approach using unitary correlation operator and high-momentum pair methods

We propose a new variational method for describing nuclear matter from nucleon-nucleon interaction. We use the unitary correlation operator method (UCOM) for central correlation to treat the short-range repulsion and further include the two-particle two-hole (2p2h) excitations of nucleon pair involving a large relative momentum, which is called 'high-momentum pair'(HM). We describe nuclear matter in finite size with finite particle number on periodic boundary condition and increase the 2p2h configurations until we get the convergence of the total energy per particle. We demonstrate the validity of this 'UCOM+HM' framework by applying it to the symmetric nuclear and neutron matters with the Argonne V4$^\prime$ potential having short-range repulsion. The nuclear equations of state obtained in UCOM+HM are fairly consistent to those of other calculations such as Brueckner-Hartree-Fock and auxiliary field diffusion Monte Carlo in the overall density region.

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arXiv2018

Contact representation of short range correlation in light nuclei studied by the High-Momentum Antisymmetrized Molecular Dynamics

The high-momentum antisymmetrized molecular dynamics (HMAMD) is a new promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics in describing the high momentum correlations in various nuclear states. In the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a new formulation by including a new Gaussian weighted basis of high momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that the very high-momentum components in the new HMAMD basis are found to be almost equivalent to the contact representation of the nucleon-nucleon pairs with very small nucleon-nucleon distance. The explicit formulation for the contact term significantly improves the numerical efficiency of the HMAMD method, which shows the importance of the contact correlation in the formulation of light nuclei.

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arXiv2018

The tensor-optimized high-momentum antisymmetrized molecular dynamics with bare interaction and its application in ${}^{4}$He nucleus

We formulate the "tensor-optimized high-momentum antisymmetrized molecular dynamics (TO-HMAMD)" framework for ab initio calculations of nuclei by hybridizing the tensor-optimized (TO-) and high-momentum (HM-) AMD approaches. This hybrid approach has advantages in both analytical simplicity and numerical efficiency comparing with other AMD-based methods which treat the bare interaction, especially for heavier nuclear systems. In this work, the $s$-shell nucleus $^{4}$He is calculated with TO-HMAMD by including up to double product of nucleon-nucleon ($NN$) correlations, described by using high-momentum pairs and spatial correlation functions of nucleons. The total energy and radius of $^{4}$He nucleus are well reproduced using the AV8$^\prime$ interaction. The spin-isospin channel dependence is also discussed for $NN$-correlations, which are found to be mostly contributed in the even-state channels, especially the triplet-even channel. Analyses of the analytical formation and numerical results suggest that TO-HMAMD could be a promising framework for general nuclear systems.

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arXiv2018

A nuclear matter calculation with the tensor optimized Fermi sphere method using central interaction

The tensor optimized Fermi sphere (TOFS) method is applied first for the study of the property of nuclear matter using the Argonne V4' $NN$ potential. In the TOFS method, the correlated nuclear matter wave function is taken to be a power-series-type of the correlation function $F$, where $F$ can induce central, spin-isospin, tensor, etc.~correlations. This expression has been ensured by a cluster expansion theory. In the TOFS calculation, we take into account the contributions from all the many body terms arising from the product of the nuclear-matter Hamiltonian $\mathcal{H}$ and $F$. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced, in comparison with other methods such as the Brueckner-Hartree-Fock (BHF) approach.

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arXiv2018

High-momentum antisymmetrized molecular dynamics compared with tensor-optimized shell model for strong tensor correlation

We treat the tensor correlation in antisymmetrized molecular dynamics (AMD) including large-relative-momentum components among nucleon pairs for finite nuclei. The tensor correlation is described by using large imaginary centroid vectors of Gaussian wave packets for nucleon pairs with opposite directions, which makes a large relative momentum. We superpose the AMD basis states, in which one nucleon pair has various relative momenta for all directions; this new method is called "high-momentum AMD" (HM-AMD). We show the results for $^4$He using the effective interaction having a strong tensor force. It is found that HM-AMD provides a large tensor matrix element comparable to the case of the tensor-optimized shell model (TOSM), in which the two-particle-two-hole (2p-2h) excitations are fully included to describe the tensor correlation. The results of two methods agree with each other at the level of the Hamiltonian components of $^4$He. This indicates that in HM-AMD the high-momentum components described by the imaginary centroid vectors of the nucleon pair provide the equivalent effect of the 2p-2h excitations for the tensor correlation.

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arXiv2017

Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call "HM-TOAMD". In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon-nucleon interaction AV8', we sufficiently reproduce the energy and radius of the 3H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method.

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