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2

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 ...

4

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 $$(E-H)G=e^{ik|r-r'|}\delta(r-r')=\delta(r-r')$$

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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 ...

0

"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 ...

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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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