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

An exact relation which links the ideal model space to be used in A-body calculations when the two-body interaction is given in a truncated model space is derived. Its implications on the effective field theory (EFT) approach to no-core-shell-model (NCSM) is analyzed. Some insights regarding whether details of two-body interaction becomes less important in the calculations of many-body system are given. The result suggests that there might be a way to establish an EFT expansion for heavy nuclei and nuclear matter with an effective intereaction which has a much simpler form than the nucleon-nucleon (NN) interaction in the vacuum.