Many-body correlations and the truncation of the shell-model Hilbert space

Three- and four-body correlations arising because of the truncation of the configuration space are calculated. These are found to be rather small. Interestingly, three-body and four-body parts of the correlations in general have opposite signs and cancel each other. Only rarely these add and become significant. This, therefore, lends support to the usage of the effective two-body interactions in the nuclear structure calculations in relatively small model spaces. It is also explicitly demonstrated through the results of the approximate shell-model calculations using broken-pair formalism.