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When I started teaching in University of Hyderabad,
very early in my teaching career, (1980),
I was to teach Nuclear Physics first time.
I had an excellent course in Nuclear Physics by Professor G, K. Mehta at IIT Kanpur.
I decided to include a detailed treatment of nucleon nucleon scattering.
I was asking the same question which every one asks:
What area is cross section?
Internet had not yet been invented. Google did not exist.
Combed through books in library which already had an excellent
collection in a short period of less than two years of its existence.
My search ended with
"Thomson Scattering as an Illustration of the Wave and Corpuscular Concepts of Cross Section"
Appendix A in R. D.Evans "The Atomic Nucleus" Tata McGraw Hill Publishing Co. (1955)
As a bonus found definition and discussion cross section for waves.
You always learn something extra from Masters..
How do you measure total cross section?
A newbie, or some one who is a hardcore theoretical physicist,
far removed from reality of experimental world, would think that one would
measure differential cross section and "sum" up over all solid angles.
Well well, this is not the way total cross section is measured.
Again Evans devotes a few pages to this. In the process and
you get a better understanding of cross section.
Evans does not stop here.
When you go to quantum theory, since everything has dual nature.
So which definition for cross section you would start with?
Definition for waves, or definition for particles, ?
Evans tells you that you can use any one.
Both are consistent when dual nature is taken into account.
