Antisymmetrization of few-nucleon systems containing two-body clusters

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.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:2201.11877Physical Review CJan 21, 20226 citations

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries. II. N Particles

Nathan L. Harshman

arXiv:1505.00659Few-Body SystemsSep 9, 201539 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”.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:1511.07224Progress of Theoretical and Experimental PhysicsJul 1, 201539 citations

Projected Faddeev-Yakubovsky equations for theN-body problem

Nir Barnea, M. Viviani

Cluster expansion of the many-body Schr\"odinger wave function is manifested through the projected Faddeev-Yakubovsky equations. It is shown that using these equations one can formulate a systematic expansion for the wave function of finite systems in a translational invariant manner. The solution of the N-body problem at a given order becomes equivalent to solving the few-body Faddeev-Yakubovsky equations. The first two orders in this expansion are given explicitly and then solved for the case of N bosons interacting through the nucleon-nucleon Afnan-Tang S3 and Malfliet-Tjon MT-V potentials.Cluster expansion of the many-body Schr\"odinger wave function is manifested through the projected Faddeev-Yakubovsky equations. It is shown that using these equations one can formulate a systematic expansion for the wave function of finite systems in a translational invariant manner. The solution of the N-body problem at a given order becomes equivalent to solving the few-body Faddeev-Yakubovsky equations. The first two orders in this expansion are given explicitly and then solved for the case of N bosons interacting through the nucleon-nucleon Afnan-Tang S3 and Malfliet-Tjon MT-V potentials.

Physical Review CFeb 16, 200013 citations

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.