Abstract
We propose a method of describing a many-body system in terms of effective interactions and show its formal equivalence to the coupled-cluster method (CCM). A transformed hamiltonian H ̃ = e −sH e S is introduced with the cluster operator S. The hamiltonian H ̃ contains many-body interactions, and they allow to define many-body average potentials. We prove that the problem of determining the ground-state energy can be reduced to calculating two-body effective interactions and they are determined from the decoupling equation for a two-body subsystem in one- and two-body average potentials. It is shown that the exact expressions of the one- and two-body average potentials are given in terms of two-, three- and four-body cluster operators in S. The three- and four-body cluster equations and their formal solutions are also given.
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