arXiv subjects

Kiyomi Ikeda

Publications and source records attributed to Kiyomi Ikeda.

At least 19 recordsLinked to original sources

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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arXiv2017

Power series expansion method in tensor-optimized antisymmetrized molecular dynamics beyond the Jastrow correlation method

We developed a new variational method for tensor-optimized antisymmetrized molecular dynamics (TOAMD) for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion are introduced and used in the power series form of the wave function, which is different from the Jastrow method. Here, nucleon pairs are correlated in multi-steps with different forms, while they are correlated only once including all pairs in the Jastrow correlation method. Each correlation function in every term is independently optimized in the variation of total energy in TOAMD. For $s$-shell nuclei using the nucleon-nucleon interaction, the energies in TOAMD are better than those in the variational Monte Carlo method with the Jastrow correlation function. This means that the power series expansion using the correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method.

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arXiv2017

New successive variational method of tensor-optimized antisymmetrized molecular dynamics for nuclear many-body systems

We recently proposed a new variational theory of "tensor-optimized antisymmetrized molecular dynamics" (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8$^\prime$ for $s$-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of $s$-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions.

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arXiv2017

Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon-nucleon interaction AV8'. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

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arXiv2017

Successive variational method of the tensor-optimized antisymmetrized molecular dynamics for central interaction in finite nuclei

Tensor-optimized antisymmetrized molecular dynamics (TOAMD) is the basis of the successive variational method for nuclear many-body problem. We apply TOAMD to finite nuclei to be described by the central interaction with strong short-range repulsion, and compare the results with the unitary correlation operator method (UCOM). In TOAMD, the pair-type correlation functions and their multiple products are operated to the AMD wave function. We show the results of TOAMD using the Malfliet-Tjon central potential containing the strong short-range repulsion. Adding the double products of the correlation functions in TOAMD, the binding energies are converged quickly to the exact values of the few-body calculations for s-shell nuclei. This indicates the high efficiency of TOAMD for treating the short-range repulsion in nuclei. We also employ the s-wave configurations of nuclei with the central part of UCOM, which reduces the short-range relative amplitudes of nucleon pair in nuclei to avoid the short-range repulsion. In UCOM, we further perform the superposition of the s-wave configurations with various size parameters, which provides a satisfactory solution of energies close to the exact and TOAMD values.

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arXiv2015

Tensor-optimized antisymmetrized molecular dynamics in nuclear physics

We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in strongly interacting system. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model (TOSM). We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".

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arXiv2015

Structures in 9Be, 10Be and 10B studied with tensor-optimized shell model

We investigate the structures of $^{9,10}$Be and $^{10}$B with the tensor-optimized shell model (TOSM) using the effective interaction based on the bare nucleon-nucleon interaction AV8$^\prime$. The tensor correlation is treated in TOSM with the full optimization of 2p2h configurations including high-momentum components. The short-range correlation is described in the unitary correlation operator method (UCOM). It is found that the level orders of the low-lying states of $^{9,10}$Be and $^{10}$B are entirely reproduced. For $^9$Be, ground band states are located relatively in higher energy than the experiments, which indicates the missing $α$ clustering correlation in these states as seen in the case of $^8$Be with TOSM. In addition, the tensor force gives the larger attraction for $T$=1/2 states than for $T$=3/2 ones for $^9$Be. For $^{10}$Be, the tensor contribution of $0^+_2$ shows the largest value among the $0^+$ states. This can be related to the $α$ clustering correlation in this state. It is also found that the level order of three nuclei depends on the tensor force in comparison with the results obtained with the Minnesota interaction without the tensor force.

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arXiv2014

Shell and alpha cluster structures in 8Be with tensor-optimized shell model

We study the shell and alpha cluster structures in the ground and excited states of 8Be in terms of the tensor-optimized shell model (TOSM). In TOSM, the tensor correlation is optimized in the full space of 2p2h configurations involving high-momentum components. The short-range correlation is treated with the unitary correlation operator method (UCOM). We use the effective interaction based on the bare nucleon-nucleon interaction AV8$^\prime$. The 8Be states consist of two groups of ground band states and highly excited states with the isospin T=0 and T=1. It is found that the tensor contributions of the ground band states are stronger than the highly excited states and that the kinetic energies and the central contributions of the ground band states are almost twice the 4He values. These features suggest two-alpha clustering for the ground band states in 8Be. We also estimate the correlation energy of the $α$ clustering using the alpha cluster model. In the highly excited states, the calculated spectrum in TOSM reproduces the experimental level order and the relative energies of each level. This agreement suggests that those states can be interpreted as shell-like states. The level order is found to be sensitive to the presence of the tensor force in comparison with the results using the Minnesota effective interaction without the tensor force. It is also found that the tensor contributions in the T=0 states are stronger than the T=1 states, which is consistent with the state dependence of the tensor force.

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arXiv2013

Coulomb breakup reactions of $^{11}$Li in the coupled-channel $^9$Li~+~$n$~+~$n$ three-body model

We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in $^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.

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arXiv2012

Tensor-optimized shell model for the Li isotopes with a bare nucleon-nucleon interaction

We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8' interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM+UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p1/2 and p3/2 orbits of the last neutron, in 5Li is caused by opposite roles of the tensor correlation. In 6Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell model states. In 7,8,9Li, the low-lying states containing extra neutrons in the p3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s orbit to the p1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6Li.

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arXiv2011

Role of the tensor interaction in He isotopes with a tensor-optimized shell model

We studied the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8 obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM+UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the LS splitting energy observed in 5He, in which the p1/2 and p3/2 orbits play different roles on the tensor correlation. In {6,7,8}He, the low-lying states containing extra neutrons in the p3/2 orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the p1/2 orbit lose the tensor contribution due to the Pauli-blocking effect with the 2p2h states in the 4He core configuration.

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arXiv2011

Tensor-optimized few-body model for s-shell nuclei

As a new scheme of treating the tensor interaction of the nucleon-nucleon interaction, there is a proposal of a tensor-optimized shell-model (TOSM) for the study of medium and heavy nuclei. The TOSM includes the deuteron-like tensor correlation and provides quite a good reproduction of the binding energy and the size of $^4$He as compared with rigorous few body calculations. We propose a tensor-optimized few-body model (TOFM) using the spirit of the TOSM approximation in the few body framework with bare nucleon-nucleon interaction. We find that the TOFM can account for the strength of the tensor interaction very well and almost reproduces the full energy and various energy components as compared with rigorous few body calculations.

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arXiv2010

Di-neutron clustering and deuteron-like tensor correlation in nuclear structure focusing on 11Li

11Li is a Borromean nucleus, where two out of three objects as 9Li + n and two neutrons independently do not form bound systems. Two neutrons should form a di-neutron cluster in the nuclear field generated by the 9Li core nucleus. We treat di-neutron clustering by solving the two neutron relative wave function precisely by using the bare nucleon-nucleon interaction so that the spatial clustering structure is obtained quantitatively within the whole 11Li nucleus. This di-neutron clustering is an essential dynamics to form the halo structure by making a compact di-neutron cluster, which distributes loosely around the 9Li core. The di-neutron clustering is a new concept and is a general phenomenon in neutron skin and neutron halo nuclei. This quantitative description of di-neutron clustering has made it necessary to consider another important deuteron-like tensor correlation, which is caused by strong tensor interaction in the nucleon-nucleon interaction. The tensor interaction originates from pion exchange and known to provide large attraction to form the 4He nucleus. The unique feature of the tensor correlation is to make highly correlated deuteron-like excitation, which interferes with shell model like structure in a unique way. This dynamical effect removes the magic number effect and makes easy the participation of the s-wave neutrons. Hence, there are pairing and deuteron-like tensor correlations in addition to the mean field structure in 9Li. The combined system of two additional neutrons with the correlated 9Li provides the halo phenomenon, in which the di-neutron clustering develops with the help of large s-wave component caused by the deuteron-like tensor correlation. In this lecture note, we would like to introduce these two new concepts in a systematic manner and fill a gap between the halo phenomenon and the microscopic reason for this interesting phenomenon.

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