Compton · Source catalogue

20-page scan (Microsoft Print to PDF, no text layer; Step 0 OCR'd every page) of Compton's Physical Review, 2nd series, vol. 21, no. 5, May 1923, pp. 483-502, written at Washington University, St. Louis, dated December 13, 1922. Compton first reviews J. J. Thomson's classical theory of X-ray scattering, which predicts that scattered radiation has the same wavelength as the primary and that the intensity is symmetric forward and backward, and notes that experiments with hard X-rays and gamma-rays contradict this (reduced scattering, concentration on the emergent side). His own earlier explanation (a large electron whose size grows with wavelength, giving interference) is called hard to defend. He then reports that spectroscopy of secondary X-rays from graphite shows (p.3) that 'only a small part, if any' of the secondary radiation has the primary wavelength and instead a longer wavelength. He proposes the quantum hypothesis: each X-ray quantum spends all its energy and momentum on a single electron, which recoils. Conservation of momentum (Eq. 1) and energy (Eq. 2) give the scattered frequency nu_theta = nu_0/(1 + 2 alpha sin^2(theta/2)) (Eq. 3), equivalent to a wavelength shift (2h/mc) sin^2(theta/2) = 0.0484 sin^2(theta/2) Angstrom (Eq. 5), independent of the primary wavelength, with alpha = h/(m c lambda_0). The paper then derives, by a relativistic Doppler / moving-radiator argument (Figs. 2-3, Eqs. 9-10, 19-20, including the black-body check I/I' = (T/T')^4 = (nu_m/nu_m')^4), an angular intensity distribution for scattering from recoiling electrons (Eq. 27), admitted on p. 491 to rest on an assumption not rigorously proved: that the two methods (recoil momentum balance vs. an electron moving with effective velocity beta = alpha/(1+alpha)) give the same relative intensity at different angles. It also derives scattering and absorption coefficients: total energy removed is less than Thomson's by the ratio 1/(1+2 alpha); true scattering coefficient sigma_s = sigma_0 (1+alpha)/(1+2alpha)^2 and absorption due to scattering sigma_a = sigma_0 alpha/(1+2alpha)^2 (Eqs. 29-30). Experimental comparisons given: (i) Fig. 4, Mo K-alpha X-rays (0.708 A) scattered at 90 degrees from graphite and analysed with a calcite crystal spectrometer: scattered line at 0.730 A, shift 0.022 A observed against 0.024 A predicted; Compton calls the paper's results unpublished; (ii) gamma-rays from RaC scattered at different angles, wavelength measured via absorption in lead, rising from 0.022 A (primary) to 0.068 A at 135 degrees, in agreement with theory; (iii) velocities of secondary beta-rays in light elements consistent with recoil electrons; (iv) Hewlett's carbon absorption results below 0.5 A in excellent agreement; (v) Ishino's true absorption and scattering coefficients for hard RaC gamma-rays in Al and Fe: true absorption 0.021 observed vs 0.021/0.020 calculated, true scattering 0.045 and 0.042 observed vs 0.040 and 0.038 calculated from Eq. 29 (classical 0.193 and 0.187); (vi) forward/backward intensity ratio at 40 vs 140 degrees predicted about 1.10 for 0.7 A, whereas Barkla and Ayers observed 1.04, a discrepancy Compton acknowledges and attempts to explain by the wavelength dependence of ionization. The closing section (p. 502) restricts the theory to light elements because it tacitly assumes no constraining forces on the electrons, says that for bound electrons the quantum might spread over many electrons permitting interference, and says the relation of this to X-ray reflection and excess scattering is not yet clear. Acknowledges discussion with G. E. M. Jauncey. The paper is the founding publication of what is now called the Compton effect; the quantity h/(mc) is now called the Compton wavelength. Corrections and additions after QE. (1) The fraction of energy removed from the primary beam is sigma_0/(1+2 alpha) (Eq. 28; abstract 'in the ratio 1/(1+2a)'); the (1+2 alpha)^2 factor belongs to the true-scattering coefficient of Eqs. 29-30, not to the energy removed. (2) Gamma-ray wavelengths are inferred from absorption in lead, not measured with a spectrometer. Table I (journal p.~496, OCR p.14), observed / calculated wavelengths in Angstrom: primary 0.022 (0.022); 45 deg 0.030 / 0.029; 90 deg 0.043 / 0.047; 135 deg 0.068 / 0.063. (The digest wrongly lists observed 0.029 and 0.047, which are the calculated values; also wrongly gives the Barkla-Ayers ratio as 90/140 deg when the text says 40/140 deg.) (3) Compton reverses his own earlier position: a footnote on p.3 says that in 1921 (Phil. Mag. 41, 749; Phys. Rev. 18, 96) he had defended the fluorescence-admixture explanation of the softening, that Gray (1913, 1920) and Florance (1914) had argued for true scattering, and that the latter is 'the correct one'; the Discussion drops his own large-electron hypothesis as superfluous. (4) He admits recoil electrons from ordinary X-rays had not been observed (p.14). (5) The 0.022 A primary gamma wavelength is anchored by his own 0.025 A from small-angle gamma scattering by lead (Phil. Mag. 41, 777, 1921) and Ellis's beta-ray lines (0.045, 0.025, 0.021, 0.020 A) (p.14) [read: OCR text p.14]. (6) Fig. 7 deep read [read: page image p.18, read-offs +/-0.01]: eight filled dots (text says circles), no error bars, gamma rays scattered by iron, ionization taken as intensity under an admitted assumption ('not clear ... appears probable'). The 90 deg datum is 0.074 x classical = 0.037 I_0 [read: p.19] against Eq. 27 about 0.069 I_0 [calc]; the dots lie 20-45% below Eq. 27 from about 75 to 150 deg and about 20% above it at 60 deg; all lie 12-35x below the classical curve. Hence 'beautiful agreement' is fair qualitatively, not quantitatively. Eq. 27 exponent is 5, not 4 (digest OCR slip). Second QE round (deep reads, page images). (7) Eq. 1 (p.4) prints a PLUS before the cross term 2(h nu_0/c)(h nu_theta/c) cos(theta); Fig. 1B shows theta as the interior angle between the incident and scattered momenta (the true scattering angle), so the law of cosines requires a MINUS. This is a real printed error (not OCR); it does not propagate, since Eq. 3 is the correct result [read: page image p.4]. Fig. 1B also has arrowheads at both ends of its base, a drawing slip. (8) Eq. 23 (p.10): lines 1-2 print 2 pi R^2 but the final numbered line prints 16 pi R with no square, a real printed slip (not OCR); dimensionally the intensity needs R^2, and a SymPy substitution with beta = alpha/(1+alpha) shows the rest of the expression, including (1+2 alpha) and the fifth power, is algebraically correct [read: page image p.10; calc]. The earlier suspicion of an OCR artefact is closed. (9) Fig. 4 (p.13): no separate unshifted K-alpha peak is resolved; the scattered curve is one broadened peak displaced a few tenths of a degree, with a small shoulder at about 6.0-6.2 deg that also appears in the primary curve (by position likely Mo K-beta [memory: medium]). Resolution is poor, heights are normalised and there are no error bars, so the figure shows 'not resolved', not 'absent'; the 0.022 vs 0.024 A shift is an 8% difference with no quoted uncertainty [read: page image p.13]. (10) Table I (p.14) headings: Angle | mu/rho | tau/rho | lambda obs. | lambda calc.; values confirmed from the image: primary 0 deg .076, .017, 0.022; 45 deg .10, .042, .030 vs 0.029; 90 deg .21, .123, .043 vs 0.047; 135 deg .59, .502, .068 vs 0.063. The 'observed' wavelengths are derived from tau/rho proportional to lambda^3 scaled to the primary 0.022 A (reproduced to 0.0298, 0.0425, 0.0680 [calc]), so they are inferences, not spectrometer readings; Eq. 31 gives 0.0291, 0.0462, 0.0633 (the printed 0.047 at 90 deg should round to 0.046, trivial); obs minus calc is +0.001 (45 deg; observed higher), -0.004 (90 deg) and +0.005 A (135 deg), with no systematic trend. The primary 0.022 A is tuned within the spread of external values (Compton's own 0.025 A; Ellis lines 0.045, 0.025, 0.021, 0.020 A), and the gamma beam is a mixture of lines [read: page image p.14]. (11) Fig. 7 extra: the drawn Eq. 27 curve at large angles lies above the printed formula evaluated at alpha about 1.10 (about 0.046 vs 0.034 at 150 deg; about 0.040 vs 0.030 at 180 deg), cause not identified; against the computed formula the dots at 120-150 deg are about 25% low, against the drawn curve about 40-45% low [read: page image p.18; calc]. The text calls the eight points 'circles'; they are filled dots, unevenly spaced (about 28 to 150 deg), none at 180 deg; the scatterer is iron, not a light element. Ordinary X-ray recoil electrons had not been observed; v_max = 2 c alpha(1+alpha)/(1+2 alpha+2 alpha^2), zero for forward scattering; the claim that most secondary beta-rays are recoil electrons rests on Compton's own earlier report (Bull. N.R.C. No. 20, 1922) [read: p.14]. Still not dedicated page-image reads: Fig. 5 and the p.17 forward/backward passage.

Key claims

• When an X-ray quantum is scattered by a light-element electron through angle theta, its wavelength increases by (2h/mc) sin^2(theta/2) = 0.0484 sin^2(theta/2) Angstrom, independent of the incident wavelength.
• A radiation quantum carries momentum h*nu/c as well as energy h*nu, and is scattered as a whole by a single electron that recoils with the momentum difference.
• For Mo K-alpha X-rays (0.708 A) scattered at 90 degrees by graphite, the scattered wavelength is 0.730 A, a shift of 0.022 A observed against 0.024 A predicted.
• For hard gamma-rays from RaC, with wavelengths inferred from lead absorption, the scattered wavelength grows with scattering angle, from 0.022 A (primary) to 0.068 A observed (0.063 calculated) at 135 degrees (Table I).
• The scattered radiation is concentrated in the forward direction according to Eq. 27, because the recoiling electrons move along the primary beam.
• The true scattering coefficient is sigma_0 (1+alpha)/(1+2 alpha)^2 and the scattering absorption coefficient is sigma_0 alpha/(1+2 alpha)^2, so both fall below the classical Thomson value sigma_0 at short wavelength, matching Ishino's and Hewlett's data; the total energy removed from the beam is sigma_0/(1+2 alpha).
• Classical Thomson scattering cannot explain a wavelength change, because a classically forced electron re-radiates at exactly the incident frequency.
• The theory applies only to scattering from loosely bound electrons in light elements; bound electrons in heavy elements require a different treatment.
• Hard gamma-rays scattered by iron at 90 degrees have intensity 0.074 of the classical value (0.037 I_0), against about 0.07 I_0 from Eq. 27; the measured points sit below Eq. 27 at large angles.
• Compton states that the softened secondary X-rays are true scattering and not fluorescence, reversing his own 1921 view.
• Eq. 1 as printed has a plus sign before the cross term, but Fig. 1B's interior angle theta requires a minus (law of cosines); the misprint does not propagate because Eq. 3 is correct.
• Eq. 23 as printed ends with 16 pi R rather than 16 pi R^2, a printed slip; with R^2 restored and beta = alpha/(1+alpha) the reduced expression is algebraically equivalent to the unreduced line.
• Fig. 4 shows the scattered Mo K-alpha line as one broadened peak shifted by about 0.2 deg of glancing angle, with no resolved unshifted peak, but resolution and the lack of error bars do not exclude a minor unmodified component.
• The 'observed' gamma-ray wavelengths of Table I (0.030, 0.043, 0.068 A) are inferred from absorption coefficients scaled by tau/rho proportional to lambda^3 to the primary 0.022 A, not measured directly; observed minus calculated is +0.001, -0.004, +0.005 A at 45, 90, 135 degrees.
• In Fig. 7 the eight iron gamma-ray points lie about 20-45% below the Eq. 27 curve from about 75 to 150 degrees and about 20% above it at 60 degrees, with no error bars, while lying 12-35 times below the classical curve.

Relevance: This is the only document in the folder and the whole project. It is the original statement of the claim that light behaves as particles carrying momentum in scattering, now called the Compton effect (Nobel Prize in Physics 1927 shared with C. T. R. Wilson) [memory: high].

Mainstream conflict: none. It conflicted with the classical electrodynamics of 1922 (Thomson scattering) and with the then-prevailing wave picture of light, and was initially contested (e.g. by W. Duane and by Bohr-Kramers-Slater, which allowed statistical-only energy conservation) [memory: medium]; the Compton shift formula is standard textbook physics today [memory: high]. The paper's Eq. 27 angular distribution was later superseded by the Klein-Nishina formula (1929) [memory: medium].