Talk:Rutherford scattering experiments

Big theta or little theta?

@Johnjbarton: In the section Target recoil, shouldn't you use little theta ($\theta$) instead of capital ($\Theta$)? Kurzon (talk) 23:20, 12 February 2025 (UTC)

I did not find the last formula in that section on the page of the sources indicated by the citation. I tracked that last formula down to a time before I edited the page. It had no source then. Somehow Goldstein was tacked on by mistake. I corrected the current article, thanks. Johnjbarton (talk) 01:13, 13 February 2025 (UTC)

$\Theta$ or $\theta$ Kurzon (talk) 04:17, 13 February 2025 (UTC)

The only remaining formula involving angles in the section Target recoil should use capital theta, an indication that the angle is not a microscopic angle but rather one in the lab coordinates. That formula matches the source. Johnjbarton (talk) 04:32, 13 February 2025 (UTC)

Deleted historically irrelevant section

I deleted the section which provides an alternative way to work out the scattering angle. I looked through some of the books Johnjbarton referenced and saw that the mathematics for the general theory of scattering are way more complex than what this article provides and therefore this section was a little silly. I have however kept the section which explores the scattering angle from a hyperbolic geometry approach because it is historically relevant, it's what Rutherford (probably) used. This is a history article, not a general article on scattering theory. Kurzon (talk) 16:46, 13 February 2025 (UTC)

We agreed to move content from Rutherford scattering to this article. Now you want to delete it. I disagree. Rutherford scattering redirects here and that is the technical term for the kind of scattering he discovered.

If you want to split out the scattering model work we can discuss that.

As for historical relevance, we should revisit the concept that the Rutherford proved Thomson "wrong". It is not historically correct. Johnjbarton (talk) 17:04, 13 February 2025 (UTC)

I am deleting stuff that I added in the first place, and which I now think is superfluous. Kurzon (talk) 18:31, 13 February 2025 (UTC)

The content is not yours to delete. Once added it is "ours". Johnjbarton (talk) 18:35, 13 February 2025 (UTC)

Proposal to split out technical content to article Coulomb scattering

@Kurzon has argued above that technical content in this article is out of place. Rather than delete half of it, I propose we split the content roughly at "Rutherford's scattering model", put the last part into Coulomb scattering, and replace it in this article with a non-mathematical summary of Rutherford's historical paper. The Coulomb scattering article would have a summary of this article as part of its history section.

In addition to solving the issue of technical content here, the current redirect of Coulomb scattering to this article does not reflect physics sources. Coulomb scattering was made essential by Rutherford's work but it has broad implications for physics. Content related to Coulomb scattering does not fit here.

If @Kurzon agrees I will post this for broader input. Johnjbarton (talk) 18:47, 13 February 2025 (UTC)

You keep missing the point. I am only deleting some technical stuff, not all of it. Specifically, the redundant un-historical stuff. Kurzon (talk) 18:56, 13 February 2025 (UTC)

I do not believe I misunderstand you. Rather, I disagree with you.

Contrary to your claim, this is not solely a historical article at present. Both Coulomb scattering and Rutherford scattering redirect to this article. My proposal is to change this article into a purely historical article in line with your goal. The content you wish to delete may have value in the context of Coulomb scattering, even if it is not historical. Johnjbarton (talk) 19:20, 13 February 2025 (UTC)

What is the value? Kurzon (talk) 19:22, 13 February 2025 (UTC)

The value of the alternative is established by the hyperphysics site and Beiser book references. These sources chose this presentation over Rutherford's. My guess is that these sources thought students would be more receptive to a description based on forces. Forces are taught first in physics and only later do students encounter physics arguments based on energy. The energy/momentum arguments are effective for more kinds of problems, but the force approach is more intuitive. These same consideration apply to Wikipedia. Johnjbarton (talk) 19:31, 13 February 2025 (UTC)

Splitting proposal

I propose that the article be split with the content from the section "Rutherford's scattering model" on moving to Coulomb scattering. The historical experiments described in the first part of the article are a distinct notable topic from the technical content on scattering which follows.

Coulomb scattering is itself a notable physics topic. Many physics sources cover the topic of the Rutherford's experiments within a discussion of Coulomb scattering. For example, the sources Goldstein, Beiser, or Tong listed as references. Many similar examples can be found, eg Podgorsak, E. B., & Podgoršak, E. B. (2016). Coulomb Scattering. Radiation Physics for Medical Physicists, 79-142.

The current article is unbalanced, with much more content and references on history than on the physics of Coulomb scattering. We are missing coverage of topics like de Broglie wavelength, relativistic and quantum corrections, multiple scattering, relations to diffraction, Mott scattering, Møller scattering, Bhabha scattering, and topics like characteristic scattering distance.

The historical part of this article is in excellent shape such that the History section of "Coulomb scattering" needs only a summary. Conversely this article could have a non-technical summary of Rutherford's 1911 paper linking the content in the Coulomb scattering article.

Please reply Split or Keep with your reasoning. Thanks! Johnjbarton (talk) 19:05, 16 February 2025 (UTC)

Split per nom, though I am confused by why Rutherford scattering does not have its own article. ZergTwo (talk) 19:14, 16 February 2025 (UTC)

For clarification, I am asking why the phenomenon of the experiment lacked an independent article when this discussion began. ZergTwo (talk) 04:57, 27 February 2025 (UTC)

My version: We had Rutherford scattering and Rutherford scattering experiments. (The 'experiments' article had been renamed multiple times I believe). Kurzon started improving the 'experiments' article and I started improving the scattering article. At some point we disagreed about what content should be in the 'experiments' and merged the two as a compromise. Kurzon continued to make improvements in the 'experiments' article. Recently Kurzon removed the specific mathematical treatment (Alternative derivation) from 'experiments' that had triggered our disagreement in the first place. According to Kurzon, the reason is "This is a history article, not a general article on scattering theory." Since I think we should have had a separate scattering article all along I agree that the content is out of place here and proposed the split.

I want to emphasize that we currently have an excellent long article with a mix of history and scattering theory. We are missing pieces on the scattering theory. By splitting we can create two excellent articles. Johnjbarton (talk) 17:02, 27 February 2025 (UTC)

Don't split yet. First, do whatever it is you want to do in the Coulom scattering article and once it's mature, we will discuss what to trim from this article. Kurzon (talk) 19:06, 27 February 2025 (UTC)

Opposed as I need more explanation first. Are you referring specifically to scattering of heavy particles by a Coulomb field or what? Ultra-relativistic scattering by the nuvleus? Parts of what you mention are already in electron diffraction, electron scattering and electron energy loss spectroscopy. The diffraction article has only a vague mention of charged particles, and there is already a dynamical diffraction page but that is only for x-rays. The electron diffraction page has a brief mention of dynamical electron diffraction, and there are some bits in multislice (and maybe some in the other EM/ED pages). Writing a proper page on dynamical electron diffraction has been on my to-do list for a bit, but seems to be quite different from what you are suggesting. Writing an article of the current relativistic EELS would be useful, but is also different.

Can you please be more specific. Ldm1954 (talk) 20:08, 16 February 2025 (UTC)

I am referring to general undergraduate physics level Coulomb scattering as represented by the technical content in this article. I don't propose to include any significant content additions that overlap any existing article like the ones you mention. Rather I propose to include summaries that leads readers from the simple generic scattering to the many applications and extensions. The Podgorsak reference above has rough the scope I have in mind. (This is just a random reference, I don't claim it is special other than being technical and in surveying the topic without going too deep on any aspect.)

I hope that makes my suggestion clearer: the technical content here and connections to the broader issues and applications. Johnjbarton (talk) 20:34, 16 February 2025 (UTC)

That's fine with me. What I worry will happen, if you remove all the maths from this article, is that a student who comes here looking for mathematical answers as to why Rutherford's results refuted the Thomson model will not go to the Coulomb scattering article, and if they do they will feel overwhelmed by the material there which is supposed to be a general treatment. So in this article I want to keep some maths that is sharply focused on Rutherford and Thomson's work. This, BTW, is also why I would like to remove the Beiser stuff. Kurzon (talk) 20:56, 16 February 2025 (UTC)

I'm OK with this idea so long as I get to keep the maths stuff that pertains to the historical material. Namely, the stuff in the sections Rutherford's scattering model and Why the plum pudding model was wrong. Johnjbarton can then make the Coulomb scattering article a more general article on particle scattering. Kurzon (talk) 20:33, 16 February 2025 (UTC)

In my opinion the historical story line in this article does not benefit from the detailed math treatment in the latter part of the article. By replacing the math in these sections with a summary of physics in Rutherford's paper, the content would be better aligned with the earlier half of the article. The key aspects of Rutherfords theory and why it differed from Thomson's (and Bohr's) can be presented without discussing the equations of hyperbolic trajectories. On the other hand, the detailed equations are vital for the technical content on Coulomb scattering, but we can keep all of the existing material together as it is in great shape. Johnjbarton (talk) 16:29, 20 February 2025 (UTC)

Split. The fully quantum treatment of Coulomb scattering is a standard textbook topic, and there are multiple approaches that deserve encyclopedic coverage. (I am away from my office bookshelf, but going from memory, Griffiths and Sakurai treat Coulomb scattering as a limit of Yukawa scattering, and Schiff and/or Baym do it in a more rigorous but more demanding way by separating the Schroedinger equation in parabolic coordinates.) Coulomb scattering is a topic in its own right, and an article under that name would have room for expansion without having to squeeze everything into the context of particular experiments from the 1910s. XOR'easter (talk) 21:00, 16 February 2025 (UTC)

Yeah, that's my point: a general article will be too complicated for someone who just wants a straight answer on why Rutherford's experiments refuted the Thomson model. So let me keep most of the maths here. We shouldn't split the article, more like create an extension. Kurzon (talk) 21:13, 16 February 2025 (UTC)

I don't really follow. A reader who just wants a straight answer on why Rutherford's experiments refuted the Thomson model would very likely be content with the summary near the beginning of the article. Anyone who is invested enough to want more mathematics will be able to click a link to read the details.

Even if the article isn't split, Coulomb scattering should be its own page, not a redirect to Rutherford scattering experiments. XOR'easter (talk) 21:42, 16 February 2025 (UTC)

So long as you keep it simple and only do a single scattering event in a very high energy limit that is OK. Note that the simple approaches in any of the textbooks mentioned above are inadequate; sometimes textbooks over-simplify. A standard benchmark is that with 100 keV electrons a single gold atom needs to be considered to about 10th order (where kinematical/Born is first order). This is why Bethe`s 1928 paper is always quoted in the ED literature to explain the Davisson-Germer/Thompson-Reid results, not de Broglie. Ldm1954 (talk) 21:50, 16 February 2025 (UTC)

I am simply proposing a split here, so you can review the existing content to see if it matches your criteria. Of course I cannot control what other editors may do in future but you can push back on future changes. Are you still opposed? Johnjbarton (talk) 23:31, 16 February 2025 (UTC)

Not opposed now you have clarified. Ldm1954 (talk) 01:57, 17 February 2025 (UTC)

Alpha particles as point particles

@Johnjbarton: Something I overlooked when writing this article is that alpha particles were not thought of as point particles before Rutherford's experiments. They were plum pudding helium atoms with two electrons missing. So an alpha particle going through a gold atom is a positive sphere going through another positive sphere. Kurzon (talk) 03:31, 26 February 2025 (UTC)

I thought we discussed this at one point. Heilbron discusses this issue. In particular Heilbron points out that Rutherford's compact charge applies to both the gold and helium atoms. In years leading up to 1911 Rutherford gathered more and more experience with alpha particles and the occasional strong backscattering kept coming up. These alpha particles are power packed and to have them bounce meant a strong response. So Rutherford had lots of hints that alpha particles were not like atoms and had to be compact.

Recall that Thomson never considered alpha particle scattering, only beta particles. He was all-electrons, all of the time ;-). So the structure of the alpha was solely an issue for Rutherford's work. Johnjbarton (talk) 03:55, 26 February 2025 (UTC)

I do recall those conversations, I was just worried that some older parts of this article needed to be revised. Kurzon (talk) 04:24, 26 February 2025 (UTC)

Comparison to JJ Thomson's results

@Johnjbarton: Could you please check up on the alterations I made here? I think my rewrite makes things more comprehensible but I might have distorted it. Kurzon (talk) 20:03, 5 March 2025 (UTC)

Generally I think these are fine.

• [1] removed the motivation for Rutherford to compare to Thomson's work. The paragraph now starts "Rutherford needed to compare his new approach to Thomson's." Why?
• [2] removed two important details about Thomson's work with a brief statement that not correct. Thomson's beta particle scattering model, presented in 1910, predicted that a beta particle could be scattered by a large angle after a series of atomic collisions. Thomson never predicts large angle scattering. I think something more like

"Thomson's beta particle scattering model, presented in 1910, predicted that a beta particle could be scattered by a very small angle requiring a series of atomic collisions to create a measurable effect." Johnjbarton (talk) 02:20, 6 March 2025 (UTC)

The cause of Thomson's miss

The article attributes Thomson's failing to his use of beta particles with less momentum than alpha. There is something to this, as outlined in Heilbron and other sources: Rutherford was lucky because his alpha particles were the right energy to penetrate the atom but not the nucleus and to scatter elastically rather than cause excitation which muddles the analysis. However, this claim is not supported by sources:

• But Thomson's scattering model could not account for large scattering when it came to alpha particles, which have much more momentum than beta particles.

Thomson's model could not account for large scattering of beta particles either.

Thomson's model was designed to explore the role of electrons, full stop. He never considers large angle scattering because he never observed any large scattering of electrons. That's why Thomson's model was not 'wrong': it accounted for the facts known to Thomson. Thomson's model was huge leap forward in science, the first model with subatomic particles.

But I digress. The sentence here would be more correct as

• But Thomson's scattering model could not account for large-angle scattering.

Johnjbarton (talk) 17:32, 7 March 2025 (UTC)