In this post, we shown that the elastics cross section is given by
For elastics scattering , so that
Before we continuous, lets introduce the scattering operator
where is the outgoing wave of the total Hamiltonian. And is the free plane wave. At very far way, a free plane wave is scattered by the scattering operator and result in different . The nuclear potential is included in the operator.
and the scattering amplitude is
For absorption,
The absorption cross section also called reaction cross section. The elastic cross section is from the real-part of the potential, and the absorption (reaction) cross section is from the imaginary-part of the potential. That means, part of the flux will go to the absorption (reaction) channels from the elastics channel.
For elastic scattering, , thus, no absorption. Maximum elastic cross section when , and no elastic cross section when .
The relation between and is plot below, where .
When , both elastics and absorption cross section is equal. The horizontal line is the step for from 0, to 1. The curved lines are step for from 0, 90 deg.
We can see that, the elastic scattering can be 4 times more, this is when the scattering is constructive interfered, i.e. . And the elastic scattering can be 0. time is when the scattering is destructive interfered.
There can be elastics scattering but not reaction scattering (or absorption). But whenever there is reaction scattering, elastics scattering is there.