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.
Shell and cluster structures in $^{20}$Ne in the variation of multiple bases of the antisymmetrized molecular dynamics
Osaka Institute of Technology（大阪工业大学）；Osaka University（大阪大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Huzhou University（湖州学院）；Hosei University（法政大学）；South China University of Technology（华南理工大学）；Osaka Medical and Pharmaceutical University（大阪药科大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）
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
General Education, Faculty of Engineering, Osaka Institute of Technology（大阪工业大学工学部一般教育）；Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）
