Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:nucl-th/0607059 · Progress of Theoretical Physics

Tensor Correlation in 4He with the Tensor-Optimized Shell Model

Takayuki Myo, Satoru Sugimoto, Koji Kato, Hiroshi Toki, K. Ikeda

Published Feb 1, 2007• 52 citations
arXivHTMLPDF

Abstract

We study the characteristics of the tensor correlation in 4 He using a shell model type method.We treat the tensor force explicitly by performing a configuration-mixing calculation in the 2p2h basis and include single-particle states up to intermediately high angular momenta.We adopt the Gaussian expansion method for the quantitative description of the spatial shrinkage of the single-particle states to optimize the tensor correlation.We are able to describe the full strength of the tensor correlation for 4 He in the shell model type method by realizing convergence.We call this model the tensor-optimized shell model.It is found that in 4 He, three specific 2p2h configurations are strongly coupled with the (0s) 4 configuration due to the characteristic features of the tensor operator.

DOI
10.1143/ptp.117.257

Related papers

Short-Ranged Central and Tensor Correlations in Nuclear Many-Body Systems

Thomas Neff

In this work a unitary correlation operator is presented that explicitly describes the short-ranged central and tensor correlations in the nuclear many-body system. These short-ranged correlations are induced by the repulsive core and the pronounced tensor force of realistic nucleon-nucleon interactions and cannot be described by the simple many-body states of a mean-field or shell model approach. The unitary correlation operator is discussed for the Argonne V18 and the Bonn-A interactions. Applying the correlation operator onto the Hamiltonian a common effective interaction for low momenta is obtained. Calculations for 4He using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. Calculations for 16O and 40Ca which are not possible with exact methods are performed using harmonic oscillator shell model states. The observed deviation from the experimental binding energies and radii is attributed to the missing three-body forces. The correlated interaction in a basis-free representation is used in the Fermionic Molecular Dynamics model to calculate the nuclei of the p- and the sd-shell. In this model the uncorrelated many-particle state is given as a Slaterdeterminant of Gaussian wave-packets with spin and isospin degrees of freedom which allows a consistent description of spherically symmetric, intrinsically deformed and clustered nuclei.

•Jan 1, 2008•5 citations

Tensor-optimized antisymmetrized molecular dynamics in nuclear physics: Table 1.

Takayuki Myo, Hiroshi Toki, Kiyomi Ikeda +2 more

We develop a new formalism to treat nuclear many-body systems using the bare nucleon–nucleon interaction. It has become evident that the tensor interaction plays an important role in nuclear many-body systems due to the role of the pion in strongly interacting systems. 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. 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”.

arXiv:1511.07224•Progress of Theoretical and Experimental Physics•Jul 1, 2015•39 citations

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

Takayuki Myo, Mengjiao Lyu, Hiroshi Toki +1 more

Abstract 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.

arXiv:2102.00638•Progress of Theoretical and Experimental Physics•Jan 5, 2021•6 citations

Entanglement and correlation in two-nucleon systems

Kruppa, András Tibor, Kovács, József, Salamon, Péter +1 more

We examine the mode entanglement and correlation of two fermionic particles. We study the one- and two-mode entropy and a global characteristic, the one-body entanglement entropy. We consider not only angular momentum coupled states with single configuration but use the configuration interaction method. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures. We show that when the total angular momentum is zero specific single configurations describe maximally entangled states. It turns out that for a finite number of associated modes the one- and two-mode entropies have identical values. In the shell model framework, we numerically study two valence neutrons in the $sd$ shell. The one-body entanglement entropy of the ground state is close to the maximal value and the associated modes have the largest mutual information.

•Jan 1, 2021•21 citations

Entanglement and correlation in two-nucleon systems

A T Kruppa, J Kovács, P Salamon +1 more

Abstract We examine mode entanglement and correlation of two fermionic particles analytically and numerically. We study the one- and two-mode entropies and a global characteristic, the one-body entanglement entropy considering angular momentum coupled state with a single configuration. We show that with rearrangement of the single-particle orbitals the Slater decomposition can be obtained which can also be applied for configuration mixing subject to special restriction. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures, which becomes very simple for zero total angular momentum. The Slater decomposition allows us to define associated modes, and it turns out that they have identical one- and two-mode entropies. Furthermore, we show that specific single configurations describe maximally entangled states when the total angular momentum is zero. The numerical shell model study of two valence neutrons in the sd shell is revealed that the one-body entanglement entropy of the ground state is close to the maximal value, and the associated modes have the largest mutual information.

arXiv:2006.07448•Journal of Physics G Nuclear and Particle Physics•Oct 20, 2020•32 citations

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

Takayuki Myo, Mengjiao Lyu, Hiroshi Toki +5 more

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 provide 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.

arXiv:2201.11877•Physical Review C•Jan 21, 2022•6 citations
We study the characteristics of the tensor correlation in 4 He using a shell model type method.We treat the tensor force explicitly by performing a configuration-mixing calculation in the 2p2h basis and include single-particle states up to intermediately high angular momenta.We adopt the Gaussian expansion method for the quantitative description of the spatial shrinkage of the single-particle states to optimize the tensor correlation.We are able to describe the full strength of the tensor correlation for 4 He in the shell model type method by realizing convergence.We call this model the tensor-optimized shell model.It is found that in 4 He, three specific 2p2h configurations are strongly coupled with the (0s) 4 configuration due to the characteristic features of the tensor operator.
In this work a unitary correlation operator is presented that explicitly describes the short-ranged central and tensor correlations in the nuclear many-body system. These short-ranged correlations are induced by the repulsive core and the pronounced tensor force of realistic nucleon-nucleon interactions and cannot be described by the simple many-body states of a mean-field or shell model approach. The unitary correlation operator is discussed for the Argonne V18 and the Bonn-A interactions. Applying the correlation operator onto the Hamiltonian a common effective interaction for low momenta is obtained. Calculations for 4He using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. Calculations for 16O and 40Ca which are not possible with exact methods are performed using harmonic oscillator shell model states. The observed deviation from the experimental binding energies and radii is attributed to the missing three-body forces. The correlated interaction in a basis-free representation is used in the Fermionic Molecular Dynamics model to calculate the nuclei of the p- and the sd-shell. In this model the uncorrelated many-particle state is given as a Slaterdeterminant of Gaussian wave-packets with spin and isospin degrees of freedom which allows a consistent description of spherically symmetric, intrinsically deformed and clustered nuclei.
We develop a new formalism to treat nuclear many-body systems using the bare nucleon–nucleon interaction. It has become evident that the tensor interaction plays an important role in nuclear many-body systems due to the role of the pion in strongly interacting systems. 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. 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”.
Abstract We study 5^55He variationally as the first ppp-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 5^55He, 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.
We examine the mode entanglement and correlation of two fermionic particles. We study the one- and two-mode entropy and a global characteristic, the one-body entanglement entropy. We consider not only angular momentum coupled states with single configuration but use the configuration interaction method. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures. We show that when the total angular momentum is zero specific single configurations describe maximally entangled states. It turns out that for a finite number of associated modes the one- and two-mode entropies have identical values. In the shell model framework, we numerically study two valence neutrons in the sdsdsd shell. The one-body entanglement entropy of the ground state is close to the maximal value and the associated modes have the largest mutual information.
Abstract We examine mode entanglement and correlation of two fermionic particles analytically and numerically. We study the one- and two-mode entropies and a global characteristic, the one-body entanglement entropy considering angular momentum coupled state with a single configuration. We show that with rearrangement of the single-particle orbitals the Slater decomposition can be obtained which can also be applied for configuration mixing subject to special restriction. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures, which becomes very simple for zero total angular momentum. The Slater decomposition allows us to define associated modes, and it turns out that they have identical one- and two-mode entropies. Furthermore, we show that specific single configurations describe maximally entangled states when the total angular momentum is zero. The numerical shell model study of two valence neutrons in the sd shell is revealed that the one-body entanglement entropy of the ground state is close to the maximal value, and the associated modes have the largest mutual information.
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 sss-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 provide 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.