My teacher told me that the cross section is an intrinsic property and therefore should always be the same in any particle distributions. I am dubious about this. Suppose the following two cases, where in the first one the particle distribution is different from the second. It is obvious that they would have very different total cross section. Even if we concentrate on a same area, we would still expect a different differential cross section for the two cases. Can anyone help explain my teacher's argument? Would you please offer me any references describing it?