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Scattering cross sections can have other parameters besides angle. For example you commonly have cross sections vs. angle and final energy, $d\sigma/d\Omega\, dE_\text{final}$. This might reflect the fact that in a generic elastic scattering process forward-scattered particles tend to retain most of the beam energy, while backwards-scattered particles must ...


I haven't work out the math but looks like expression you get is correct, you just need to use the following identity $$ f(x)\delta^n(x)=f(0)\delta^n(x) $$ Therefore $$ (E-H)G=e^{ik|r-r'|}\delta(r-r')=\delta(r-r') $$


As what enters into the formula is $\boldsymbol q$ instead of $\boldsymbol k$, I'd say we need a high $\boldsymbol q$ (which, of course, implies a high $\boldsymbol k$, because of conservation of energy/momentum). For example, if $\boldsymbol k$ is very high, but $\boldsymbol q$ is not, this means that there was barely no scattering, which means you didn't ...


"Activation" in the neutron business refers to transmutation of stable isotopes to unstable isotopes by neutron capture, such as $\rm^{27}Al + n \to {}^{28}Al + \text{photons}$, or to other nucleon-exchange processes such as $\rm^{14}N + n \to {}^{14}C + p$. Sometime later the unstable isotope emits detectable beta (and possibly gamma) radioactivity. The ...


Check out Halzen & Martin page 91. Supose you're doing electron-muon scattering. Pf is the electron momentum in the final state, and Pi electron momentum in the initial state. You are correct that the total momentum is conserved (it is 0 before and after, in the CM frame), but the momentum of each particle changes.

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