Compton's paper was titled “A quantum theory of the scattering of x-rays by light elements”. It is a hard read by modern standards, and mixes quite a bit of theory in at first with later experimental results. The old jargon takes some tracking down, and the propensity of using wavelength in fractions of an angstrom as the unit of measure takes some getting used to.
The initial experimental test is with k-alpha emissions from molybdenum scattered off of graphite; the experimental details are later published as The Spectrum of Scattered X-rays Fun fact: They used a 1.5 kW tube. Our devices are closer to 1W. They also note that the intensity at 135 degree scattering is about 25000 times lower than the direct beam.
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| The first plot presented by Compton showing a shift in wavelength. |
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The actual data presented by Compton in the paper. In this instance, he is using RaC (Radium C aka Bismuth-214) for his gammas. The spectrum from it isn't as pure as you'd like. From what I can read, he averaged results from scattering off of iron, aluminum and paraffin for the 2nd column. WTF is going on? |
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| A plot of the data from the last two columns of the table. |
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| Compton's intensity vs angle plot. The fit isn't great, but neither is the data. |
The predicted intensity is
$$I = I\dfrac{Ne^4}{2R^2m^2c^4}\dfrac{1 + \cos^2\theta + 2\alpha (1 + \alpha)(1-\cos\theta )^2}{(1 + \alpha (1-\cos\theta))^5}$$
After showing this, he concludes “…The beautiful agreement between the theoretical and the experimental values of the scattering is the more striking when one notices that there is not one single adjustable constant connecting the two sets of values.”
Contrast to presentation of the Klein-Nishina paper, using
$$ I = I_0\dfrac{e^4}{2m^2c^4r^2}\dfrac{1 + \cos^2\theta + 2\alpha (1 + \alpha)(1-\cos\theta )^2}{(1 + \alpha (1-\cos\theta))^3}\left( 1+\left(\dfrac{h\nu}{mc^2} \right)^2 \dfrac{(1-\cos\theta )^2}{(1 + \cos^2\theta ) \left( 1 + \dfrac{h\nu}{mc^2}(1-\cos\theta ) \right) } \right) $$
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| Klein-Nishina comparing to Compton's data |
Here, the correction factor is on the order of $\left(\dfrac{h\nu}{mc^2}\right)^2 \approx 1.1$ for the energies Compton was using. They add a note in the proofreading stage that the wavelength of gammas Compton was looking at was on average half that of the most common one, which royally screws everything up. Taking the actual spectrum into account, they say that the intensity data matches their model better than Dirac's. The spectrum of Bi-214 is shown below for reference. Making matters worse, this isotope has a half-life of about 20 minutes. How the hell were they preparing it?
From what I can tell, he was probably doing something to isolate Radon and then either chemically precipitating out the bismuth or just waiting an appropriate amount of time for the quantity to peak in the sample? If it is the timing thing, he would've had a decent bit of Pb-214 in there adding in some ~300 keV gammas.
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| Bi-214 spectrum. Compton had it pegged as just 0.022 Angstrom (660 keV) gammas, so his intensities would be pretty messed up. |
Random aside: How to plot Klein-Nishina intensities in Python: https://scipython.com/blog/the-kleinnishina-formula/
He also cites another paper titled “The Degradation of Gamma-Ray Energy” in 1921