Right. That's what this statement indicated: "For ##Q\ne 0##, the non-relativistic kinematics aren't consistent. We can see this if we try to show that the total momentum is conserved in the center of mass."
You’re right about lab frame momentum conservation making it unsurprising.
But I claim it’s zero non-relativistically, which is still a bit surprising.
But maybe it shouldn’t be. For ##Q\ne 0##, the non-relativistic kinematics aren't consistent. We can see this if we try to show that the...
I was surprised this morning when I got off on a tangent regarding the amount of energy available in the laboratory frame just at threshold. It reveals an interesting relativistic effect.
Consider a reaction (I'm thinking in terms of nuclei and/or particles) ##1 + 2 \to 3 + 4 + \cdots## with...
This comment was not well constructed originally by me. The original question was about the equivalence of the terms "endothermic" and "threshold reaction" using the reaction ##^{10}B(n,2\alpha)^3H## as an example. And then I muddied the waters by using a different reaction...
I happened to stumble across this (old) question and, since the premise of the question is incorrect, I thought I should comment.
The reaction ##^{10}B(n,\alpha)^7Li## has a positive ##Q##-value (of about 2.8 MeV). This means it is exoergic (or, as it's sometimes written, exothermic -- I think...
I'm aware of this paper. It agrees with my statement above, regarding tupos' comment, that the exact (not the asymptotic expression for ##\eta = r-z \to \infty##) wave function is finite at all finite ##r##. And yes, as you point out, the exact solution is a linear superposition of two linearly...
The indefinite integral effected in this PF post (from 2010) is not the correct expression for the Rutherford differential cross section.
Here is the correct expression in a slightly different notation (so I'll try to be careful to define all the symbols).
The expression for the differential...