I am a little confused about what "Optical Limit" means in the context of hadronic diffraction.

In some text it says that is the case where $A$, $B$ goes to infinity, where $A$ and $B$ are the numbers of the nucleons in the nuclei $A$ and $B$ respectively. Why is it called "the optical limit?"

On the other hand, we have the "Optical Theorem" which relates the imaginary part of the amplitude of the wave with the total cross section. Under what conditions can I apply this optical theorem? Is it related with the optical limit?


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The differential cross section for a collision can be written as $$d\sigma/db=1-[1-T(b)\sigma_{NN}]^{AB},$$ where $T(b)$ is the also known as the thickness function or transmission coefficient. Basically, the optical limit assume that $A,B\to\infty$ so you can make the approximation $$[1-T(b)\sigma_{NN}]^{AB}\simeq \exp[-ABT(b)\sigma_{NN}].$$ Physically, this is equivalent to making each nucleon in the projectile interact only once with the target before being absorbed. I am not sure about the original meaning of the term "optical" but I guess it related to the limit where the nucleus become so absorptive like a black box.

The optical limit is not directly related to the optical theorem in the mathematical sense but I think some deeper (but less clear) connections in term of physical interpretation can be made.


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