A. INTRODUCTION

The two-nucleon interaction is known to have a strong repulsion at short range. Consequently, a perturbative approach to scattering theory or the bound-state problem cannot be based directly on the free interaction V. Early applications of the theory of direct reactions therefore substituted a nonsingular phenomenological interaction. One justification for this approach can be understood as follows: Recall from Chapter 6 that Watson (1953) and Frances and Watson (1953) achieved a reordering of the Born series for the T operator so that each nucleon-nucleon interaction is represented by the ? matrix rather than V. The ? matrix is just the two-body t-matrix defined for scattering in the nuclear medium. It describes the complete scattering sequence, iterating the effect of V to all orders. As such it is well behaved even though V may be singular. In Chapter 8 we carried out a further development in which the space of target nuclear states was divided into two classes, denoted by P and Q. The P space includes the ground and other low-lying levels of interest, but especially collective states. The Q space refers to all the other states. We saw that a formally exact solution can be obtained in the truncated space P, provided that the interaction V is replaced by a new interaction operator . This new interaction is a many-body operator and does not have the form of a sum of two-body operators,...