Non-degenerate shell-model effective interactions from the Okamoto–Suzuki and Krenciglowa–Kuo iteration methods

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−kVlow−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 Zˆ-box employed therein is well behaved while the corresponding vertex function Qˆ-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.