Three-cluster equation using the two-cluster RGM kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed into the Faddeev equation, which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with a more complete calculation using the three-cluster RGM, As a simple example, we discuss three di-neutron (3d') and 3alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3d' system.