TABLE OF CONTENTS In the last chapter, the introduction of the optical potential was motivated as a means of describing the average field experienced by the colliding nuclei. The direct nuclear reactions are then viewed as being caused by a weak interaction that induces a transition to occur between two channels, in each of which the relative motion is described by an optical potential. In this chapter, we shall derive an approximation of the transition amplitude that corresponds to this interpretation, which is known as the distorted-wave Born approximation (DWBA). This approximation is without doubt the most useful one in direct nuclear reaction theory and is valid as long as the reaction is sufficiently weak. For stronger transitions, the coupled-channel formalism offers the most useful means of going beyond first order in the interaction causing the transition. We shall come to this method in Chapter 8.
We shall derive the DWBA from a general transformation of the transition amplitude due to Gell-Mann and Goldberger, (1953). They introduce an arbitrary auxiliary potential, which is supposed to present a solvable problem. They then transform the transition amplitude so that it depends on the solution of this solvable problem. In our context, the auxiliary potential will be the optical potential.
This chapter will be devoted to the general problem of deriving the DWBA. The application to specific nuclear reactions will be taken up in Chapter 7.
Recognizing that the scattering of nuclei from each other through the effect of their...
