Also, your "conclusion" is ... rather bad
Your attempt to calculate "cross sections" is gibberish. You do some calculation "restricting yourself to head-on collisions"? And then you just pull an exponent out of this calculation and use it to replace another exponent in another formula? Nooooo. That's not how it works. You want to show some properties of a electromagnetic cross section?
Calculate the cross section, using the standard E&M methods that are used to calculate cross sections.
I have no idea why you are citing a 1824 paper by Poisson. What is it about crackpots and 19th century citations? Is something wrong with James Clerk Maxwell's equations, which in 1862 correctly packaged/summarized/unified all prior work on the subject? if so, say so. That would be a much bigger discovery than "I found a formula for Rutherford scattering". Is something wrong with the subsequent 150-year body of additional clarification, pedagogy (say, Jackson's Electrodynamics), etc. of electrodynamics? If so, say so, that would be a much bigger discovery than "I found a formula for Rutherford scattering."
I think I know why cranks go fishing in premodern literature. Modern literature is too clear about what it's doing. You pick up Jackson's Electrodynamics and right off the bat he's asking you to take carefully-constructed surface integrals over vector fields. Too hard! As a crank, what you're looking for is for a source that:
- blathers about magnets for a while
- supplies some simple formulas without being too clear about their domain of applicability
- is hard for your critics to get a hold of.
- maybe has some fame or cache so people believe it.
So, yeah, Poisson 1934 works pretty well. What exactly did he say? What did he put an exponent of 3 onto? Probably not what you say he did, Bernard, but
I'm not gonna check. Was he
right? This is early-early-early electromagnetism, people were still flailing around trying to figure it out. You're in luck, Bernard, because
I'm not going to check a French manuscript from 1934. As a crackpot, maybe that feels like a "win" in that you deflected some avenues of criticism; as a scientist, it's pretty lame. Scientists are supposed to aim for clarity, openness, and verifiability, not "immunity from criticism."
And the name "Poisson" seems to carry some cache, right? As a crackpot, you'd rather quote a famous person like Poisson Himself than quote (say)
the web page of some Georgia educators you've never heard of---although you misapprehend which one a modern physicist trusts more.
Second: wow, you are getting excited about a really crappy fit. The data you're plotting ? They don't agree with your new curve. First, the way you've drawn the curves, your "new curve" only overlays the data over a tiny tiny range---like, 25--30 MeV. Second, if there are multiple forces contributing to a cross section, you have to
add their contributions. In the presence of an "electric" force and also a "magnetic" force, the total cross section is the
sum of the two.
You draw it as though the electric force is the only thing there from 0--25 MeV, the (huge, according to the formula) magnetic cross section is just ... missing. Then (according to your plots) you
magically turn off the electric force at 25 MeV and let the magnetic force take over. (Note that you've adjusted the normalization of the curve, purely by hand I think, to make the curves meet at 25 MeV.) That's physically nonsense. If we take your cross-sections physically seriously, and
add them, we get a cross-section-vs-energy curve that's huge and falling steeply at low energies (dominated by your "magnetic" term) and then falls slowly at high energies (dominated by the "electric" term). This is the opposite of reality.