  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.
