Convergent Theory for Effective Interaction in Nuclei

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Abstract
A general equation is derived for constructing the effective interaction on the basis of the similarity transformation theory. It is proved that the equation is equivalent to Bloch's equation for the degenerate perturbation theory and, therefore, the present approach is also equivalent to the energy independent Rayleigh-Schrödinger theory. Some iteration methods are proposed to solve the equation, and the convergence conditions for the iteration procedures are discussed. Two iteration methods—self-energy insertion and vertex renormalization—are obtained to reach the true eigenvalues of the full Hamiltonian even when there are some intruder states. It is proved that the self-energy insertion procedure produces the eigenvalues of eigenstates which have large overlap with the model space. One the other hand, the vertex renormalization procedure gives the eigenvalues nearest to the unperturbed starting energy.

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