TABLE OF CONTENTS In Chapters 3, 5, and 6 we derived exact expressions for the 
matrix, and we also discussed two approximations, one based on the Born series and one on the distorted-wave Born series. The DWBA is a very valuable approximation which is widely employed in the interpretation of data from direct reactions. It is valid for transitions that are not too strong, although it is difficult to give a quantitative measure to this statement. Generally we know that transitions involving collective states are too strong to be treated in first order. The series expansions of the transition amplitude, whether the Born (6.35) or distorted Born series (6.52, 6.58), are not convenient as a means of calculating higher-order corrections, generally speaking. Each order is increasingly more cumbersome. There is an alternative to summing the series term by term that consists of developing the Schr dinger equation as a system of coupled equations. Then, subject to the approximations with which this system is obtained, its solution accounts for the interaction to all orders.
As in Chapter 3, denote by H ? the intrinsic nuclear Hamiltonian(s)
| (8.1) |  |
Denote the kinetic energy operator of relative motion by T, and the interaction by V. (Because we discuss only elastic and inelastic scattering, the channel subscript ? is not needed on T and V.)
Suppose that we have model Hamiltonian(s) for the target H A (and projectile H a) and we wish to...
