We discuss a procedure to transfer the description of a fermion system from a subspace of the full shell model space built in terms of collective pairs onto a space of corresponding bosons. We apply the procedure to systems of six nucleons in the 1s0d major shell. We perform exact shell model calculations and compare them with calculations in the collective pair and boson approximations. The effects of the truncation of the boson Hamiltonian and of the consequent violation of the Pauli principle are examined.
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