TABLE OF CONTENTS In the last chapter the amplitude for a transition of the system from one partition to another,
was derived. The general result is
This depends on the exact wave function 
that, being exact, contains a description of all processes that can occur at the given bombarding energy. Even if it were possible to compute ? ?, and hence to compute the overlap for 
, this would be an inefficient procedure. However, we cannot compute ? ? in any case. For these practical reasons, an approximation of the amplitude would be useful. Equation (3.35) showed the crudest possible approximation, which formed the basis for the earliest work on direct reactions. In this first Born approximation, the relative motion of the two parts of the system is represented by a plane wave. We now seek to lay the groundwork for improving the calculation in this respect.
The central potential U of the shell model (3.1) is used to represent the average field of all the nucleons on a particular one, and the corrections to this average are calculated by taking into account the residual interaction V ij. In much the same sense, we understand intuitively that two nuclei, as they approach each other, are deflected by the field generated by the mutual interactions of all nucleons in one nucleus with those of the other, both before and after any specific interaction exchanges energy or nucleons between them.
Thus we introduce a...
