A folded-diagram perturbation expansion for effective operators

Linked-diagram expansions for the model-space effective operators are derived for both open-shell nuclei and closed-shell nuclei. These expansions are derived using time-dependent perturbation theory and are given as a diagrammatic series which contains folded diagrams. Our results are in general agreement with the results obtained earlier by Brandow, but the general structure of the present expansions is perhaps simpler and more convenient for calculations. The projections of the true nuclear eigenfunctions onto the model space are required for the derivation of effective operators. These projections are obtained from the solution of the model-space eigenvalue problem defined by the energy-independent effective Hamiltonian. Methods for calculating the above diagrammatic series for effective operators are discussed.