Summation of time-dependent folded diagrams for effective interactions with a non-degenerate model space

We analyze the diagrammatic structure of the effective interaction for the case of a non-degenerate model space. A time-dependent folded-diagram formulation is used. It is found that the valence-linked time-ordered diagrams contained in such effective interactions can also be expressed in terms of the multi-energy Q¯-boxes of the form overlineQ_n(ɛ ₁ɛ ₂…ɛ _n+1), which were introduced by Suzuki et al. for a time-independent description of the effective interaction. A partial-fraction method for the evaluation of the multi-energy Q¯-box, in terms of valence-linked diagrams, is discussed. A generalized Krenciglowa-Kuo iteration method for summing up the folded-diagram series is also designed. A schematic mosel is solved to compare the non-degenerate theory with the usual degenerate theory. It is shown that the present approach makes a distinct improvement in the calculation of effective interactions.