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Compton: central claims

Source gap (revised). The one document, Compton_1923.pdf (Compton, Physical Review 21(5), 483-502, May 1923), has no text layer, but Step 0 OCR'd all 20 pages, so prose and numbers are readable; equations are garbled in the OCR and were read from page images. Step 1 viewed 9 page images, the reviewers viewed most of the rest, and deep reads from page images now cover p.4 (Fig. 1B, Eq. 1), p.10 (Eq. 23), pp.13-14 (Fig. 4, Table I) and pp.18-19 (Fig. 7) in deep/. Still not done: dedicated reads of Fig. 5 (p.15) and the p.17 forward/backward passage. Not obtained: the papers Compton cites or that followed (Phys. Rev. 22, 409, 1923; Ishino; Hewlett; Barkla-Ayers; Bothe-Geiger 1925; Compton-Simon 1925; Klein-Nishina 1929). Statements here about later tests rest on [memory] or the reviewers' web checks, not on those papers.

  1. A scattered X-ray quantum gives all its energy and momentum (momentum = h*nu/c) to a single electron, which recoils; light scatters as a particle in this process.
  2. The scattered X-ray has a longer wavelength, with shift lambda_theta - lambda_0 = (2h/mc) sin^2(theta/2) = 0.0484 sin^2(theta/2) Angstrom, independent of the incident wavelength.
  3. Experiment agrees: Mo K-alpha off graphite at 90 degrees shifts 0.708 to 0.730 A (0.022 observed vs 0.024 predicted), and RaC gamma-rays (wavelengths inferred from lead absorption, not a spectrometer) shift from 0.022 A to 0.068 A observed, 0.063 calculated, at 135 degrees (Table I; the 'observed' gamma wavelengths are inferred from absorption coefficients scaled to the primary 0.022 A, and observed-minus-calculated is +0.001, -0.004, +0.005 A at 45, 90, 135 degrees). In Fig. 4 the scattered line is one displaced peak with no resolved unshifted line, but resolution is poor and there are no error bars, so a small unmodified part is not excluded. The paper says only 'a small part, if any' of the scattered X-rays keeps the primary wavelength.
  4. Classical Thomson scattering, which predicts unchanged wavelength and forward-backward symmetry, fails for hard X-rays and gamma-rays; its true scattering is too high by the factor (1+2 alpha)^2/(1+alpha), where alpha = h/(m c lambda_0); the total energy removed from the beam is lower by 1/(1+2 alpha); and the quantum coefficients match Ishino's and Hewlett's data.
  5. The scattered intensity is concentrated forward (Eq. 27), derived by assuming (admitted unproven in the paper) that a recoiling electron may be treated as a moving radiator with velocity beta = alpha/(1+alpha); the Barkla-Ayers data (40 deg/140 deg ratio 1.04 observed vs about 1.10 predicted) differ by more than their error, and in Fig. 7 the iron gamma-ray points agree in shape but lie 20-45% below Eq. 27 from about 75 to 150 deg (90 deg: 0.037 I_0 measured vs about 0.07 predicted; no error bars, and the drawn curve lies above the printed formula at large angles).
  6. The theory holds only for loosely bound electrons in light elements; bound electrons in heavy elements require a different treatment.
  7. Compton reversed his own 1921 view that the softening was fluorescence and dropped his large-electron hypothesis, accepting Gray's and Florance's earlier true-scattering view; recoil electrons from ordinary X-rays had not yet been observed (p.14).

Printed slips found by the second-round deep reads (they do not change any claim): Eq. 1 (p.4) prints + where the law of cosines with the Fig. 1B interior angle theta requires -, and Eq. 23 (p.10) ends in 16 pi R where 16 pi R^2 is needed; both are real printed errors, not OCR artefacts, and Eq. 3 and the rest of Eq. 23 are correct.