  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.
