The departure of shell-model states from independent-particle states is investigated by means of transformation methods developed in previous papers. The starting point in this paper is the many-body Schrödinger equation for the nucleus in which the potential energy is assumed to arise from strong shortrange two-body interactions. As a consequence the shell-model wave function cannot be a solution of this equation, however it can be related to the actual nuclear wave function by a suitably chosen transformation operator. This operator preserves the energy and angular momentum of low-lying nuclear states; hence it is possible to examine the splitting of energy levels in the shell model space. For a closed shell plus two or three particles this is shown to originate primarily from perturbations due to two-body interactions between the particles outside the shell. The methods used also give information about the nuclear wave function and provide some justification for the use of configuration mixing in determining nuclear magnetic moments. It is noted that the successes of configuration mixing based on two-body forces provide evidence that two-body correlations dominate over many-body correlations for many properties of the nucleus.

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