A Generalized Effective Interaction

First we examine the possibility of neglecting poles of the effective interaction within the work ing interval and the consequences of such a procedure . Secondly, the effective i n t e r a c t i o n 2 4 defined in A requires exact knowledge of the mode l states; f o r example to f o r m the matrix elements of the unperturbed Green-operator W e generalize our method, to a model space with unknown model states in Section 3. In Section 4 w e use, as an example, the mode l space spanned with the states | 0 ) . Here, j 0 ) is the exact ground state of the system with N — 1 nucleons. W e attain information concerning the energy dependence of the "self energy o p e r a t o r " o f the retarded Green-function, which can b e understood as the one particle potential in the shell model f o r nuclei.