Uncorrelated scattering approximation revisited

The formalism to describe the scattering of a weakly bound projectile nucleus by a heavy target is investigated, using the Uncorrelated Scattering Approximation. The main assumption involved is to neglect the correlation between the fragments of the projectile in the region where the interaction with the target is important. It is shown that the angular momentum of each fragment with respect to the target is conserved. Moreover, when suitable approximations are assumed, the kinetic energy of each fragment is also shown to be conserved. The S-matrix for the scattering of the composite system can be written as a combination of terms, each one being proportional to the product of the S-matrices of the fragments.