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An exact relation which links the ideal model space to be used in A-bodycalculations when the two-body interaction is given in a truncated model spaceis derived. Its implications on the effective field theory (EFT) approach tono-core-shell-model (NCSM) is analyzed. Some insights regarding whether detailsof two-body interaction becomes less important in the calculations of many-bodysystem are given. The result suggests that there might be a way to establish anEFT expansion for heavy nuclei and nuclear matter with an effectiveintereaction which has a much simpler form than the nucleon-nucleon (NN)interaction in the vacuum.

The link between two-body model space and many-body model space