ABSTRACT
As emphasized in the introduction, the two-nucleon interactions which may be used with shell model wave functions are effective interactions. They bear little resemblance to the interactions between free nucleons. The effective interaction may be obtained in nuclear many body theory as the result of drastic renormalization of the interaction between free nucleons. Given a subspace of the shell model, including one or several configurations, the theory should yield matrix elements of the effective interaction in that space. To this date, however, there is no reliable way to obtain such matrix elements by using methods of many body theory. The only practical way to use the shell model for calculation of nuclear energies is to determine matrix elements from experiment. When this is carried out self-consistently, we obtain a set of matrix elements between states of the configurations considered. There is very little chance that those may be calculated from a simple potential interaction.
