Non-degenerate shell-model effective interactions from the Okamoto-Suzuki and Krenciglowa-Kuo iteration methods
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2014 Elsevier B.V. We present calculations of shell-model effective interactions for both degenerate and non-degenerate model spaces using the Krenciglowa-Kuo (KK) and the extended Krenciglowa-Kuo iteration method recently developed by Okamoto, Suzuki et al. (EKKO). The starting point is the low-momentum nucleon-nucleon interaction Vlow-k obtained from the N3LO chiral two-nucleon interaction. The model spaces spanned by the sd and sdpf shells are both considered. With a solvable model, we show that both the KK and EKKO methods are convenient for deriving the effective interactions for non-degenerate model spaces. The EKKO method is especially desirable in this situation since the vertex function Z-box employed therein is well behaved while the corresponding vertex function Q-box employed in the Lee-Suzuki (LS) and KK methods may have singularities. The converged shell-model effective interactions given by the EKKO and KK methods are equivalent, although the former method is considerably more efficient. The degenerate sd-shell effective interactions given by the LS method are practically identical to those from the EKKO and KK methods. Results of the sd one-shell and sdpf two-shell calculations for 18O, 18F, 19O and 19F using the EKKO effective interactions are compared, and the importance of an inter-space consistency between the sd and sdpf calculations is discussed.