# Compton saçılması: verification notes

File: `simulasyonlar/compton-sacilmasi.html` (rebuilt from `sablon/sablon.html`, November 2026).
Original: `kaynak-eski/compton-sacilmasi.html` (Gemini, 2025, Tailwind, ~450 lines).

## 1. Audit of the original

| # | Issue | Evidence (original) | Correct physics / fix |
|---|---|---|---|
| 1 | **Electron angle wrong at θ = 0.** At θ = 0, E′ = E, so `atan2(E′ sin θ, E − E′ cos θ)` = `atan2(0, 0)` = 0°. | l. 121 | The physical limit is φ → 90°: a grazing photon transfers a vanishing momentum perpendicular to the beam. The new code uses `φ = atan2(cos(θ/2), (1+E/mc²) sin(θ/2))`, which is the same as cot φ = (1 + E/mc²) tan(θ/2) and is well defined at θ = 0 and 180°. Test "θ → 0 limitinde elektron açısı φ". |
| 2 | Rounded constants. `HC = 1.24 keV·nm` (true value 1.239 842), `LAMBDA_C = 0.002426 nm` (2.426 310 pm), and `ELECTRON_MASS_ENERGY` is declared but never used. | l. 111 | The error is about 0.01 % in λ_C and 0.013 % in hc. That is harmless for display, but the code was not traceable to CODATA. The new code uses CODATA 2018 through `Q4.C`. |
| 3 | **Readout precision hides the effect.** Wavelengths are printed in nm with 4 decimals (0.1 pm resolution). At 500 keV, λ = 0.0025 nm, and the shift at small θ disappears in rounding. | l. 321–324 | Wavelengths are now shown in pm with 2–3 decimals. Δλ is shown explicitly. |
| 4 | **Rainbow colour for X/γ photons.** `getEnergyColor` maps 10–500 keV to an HSL hue. The incident and scattered photons get different "colours", which suggests visible light. | l. 251–258 | X/γ rays are invisible. Photons are now drawn in the neutral ink colour, wavelength is shown by wave spacing (incident spacing fixed, scattered spacing × λ′/λ, exact ratio), and every photon has a "görünmez" label. |
| 5 | Neon glows (`shadowBlur 15`), a background grid, and a canvas without devicePixelRatio scaling (blurry on HiDPI). The canvas size is set only on window resize. | l. 140–214, 269–278 | Theme-aware drawing via `Q4.col`, DPR-aware `Q4.canvas`, no glows. |
| 6 | Electron recoil distance is a fixed fraction (0.8) of the photon's travel, independent of its speed. | l. 335, 416 | The electron now moves at its true β = pc/(T + mc²) relative to the photon (c). At 17 keV, 90° the electron barely moves (β ≈ 0.05); at 662 keV it moves at up to 0.84c. |
| 7 | The flash is drawn exactly once (`phase2Started` guard), i.e. for a single frame. | l. 410–413 | Replaced with a subtle expanding ring lasting 0.45 s. Reduced motion is respected. |
| 8 | Single event only, no spectrum, no angular distribution. Compton's real evidence (a shifted line next to an unshifted line in a Bragg spectrometer) and the classical expectation are missing. | – | New tabs "Compton'un ölçümü" (spectrometer sweep, 45°/90°/135° and primary beam, classical overlay) and "Açısal dağılım" (Klein–Nishina polar plot, Monte Carlo events, θ and T histograms with Compton edge). |
| 9 | Energy range 10–500 keV, linear slider. Compton's own 17.5 keV sits at the bottom edge, and Cs-137 (662 keV) is unreachable. | l. 86 | Log slider 10 keV–2 MeV with presets Mo Kα, 100 keV, 511 keV, Cs-137, Co-60. Angular tab 1 keV–10 MeV. |
| 10 | The sign convention for the electron angle is implicit. The photon is drawn with `rotate(−θ)` (up) and the electron at +φ in canvas coordinates (down), so the drawing is correct, but the readout gives φ without saying which side. | l. 122, 357 | The new UI and Fizik tab state that φ is measured on the opposite side of the beam axis. Momentum components are checked in the tests. |

What the original got right: Δλ = λ_C(1 − cos θ), E′ = hc/λ′, T = E − E′, and the atan2 expression for φ (except at θ = 0). Energy conservation holds by construction. The physics core was sound; the main problems were presentation and missing context.

## 2. What the new version models

**Kinematics (free electron at rest), energies in keV, wavelengths in pm (hc = 1239.84198 keV·pm):**
- Δλ = λ_C(1 − cos θ), λ_C = h/(m_e c) = 2.426 310 238 67 pm
- E′ = E / [1 + (E/m_ec²)(1 − cos θ)], T = E − E′
- φ = atan2(cos(θ/2), (1 + E/m_ec²) sin(θ/2)), i.e. cot φ = (1 + ε) tan(θ/2)
- p_e = √(T(T + 2m_ec²))/c, β = p_e c/(T + m_ec²), T_max = E·2ε/(1 + 2ε)

**Cross sections:** Thomson dσ/dΩ = (r_e²/2)(1 + cos²θ), σ_T = 8πr_e²/3. Klein–Nishina dσ/dΩ = (r_e²/2)P²(P + 1/P − sin²θ) with P = E′/E, and the closed-form total σ_KN (series σ_T(1 − 2k + 26k²/5) for k < 10⁻³ to avoid cancellation). dσ/dT = 2π (dσ/dΩ) m_ec²/E′². Event mode: rejection sampling in cos θ with envelope r_e² (the maximum of dσ/dΩ is at θ = 0 for all E).

**Compton's spectrometer (amorphous-carbon impulse model):**
- Source: Mo Kα₁ 17 479.372 eV and Kα₂ 17 374.29 eV (NIST SRD 128, direct experimental), intensity 2:1.
- Calcite Bragg spectrometer, 2d = 607.12 pm, first order; sweep θ_B = 6.40°–7.25° (λ ≈ 67.7–76.6 pm), 121 points. Instrument resolution is a Gaussian, σ = 0.40 pm ("wide", 1923-like) or 0.12 pm ("narrow", resolves Kα₁/Kα₂).
- Unshifted (coherent/Rayleigh) line ∝ F(x)², x = sin(θ/2)/λ. Shifted line ∝ S(x) × (KN/Thomson). Both × (1 + cos²θ)/2. F and S for carbon are interpolated from Hubbell et al. (1975), Table I.
- S is split into a 1s part, S_1s = 2(1 − f_1s²) with a Slater 1s orbital (ζ = 5.7), and a valence part S − S_1s.
- Valence Compton profile: Gaussian, σ = 0.9 a.u. Core: hydrogenic 1s profile J(q) = 8/(3πZ)/(1 + q²/Z²)³, Z = 5.7, cut off where the energy transfer is below the 284 eV K binding energy.
- Doppler mapping δλ = 2λ sin(θ/2)·p_z/(m_ec) (p_z in a.u. × α).
- Classical overlay: the same total intensity (F² + S), all at the incident wavelength.
- Counts: peak ≈ 420 counts at 90° plus a flat background of 8, with Poisson noise. The primary beam uses a separate scale, as in Compton's figure.

Resulting peak-height ratio (shifted/unshifted): about 1.1 at 45°, 1.9 at 90° and 2.8 at 135°. So the shifted line strengthens with angle, as Compton reported in Phys. Rev. 22, 409.

**Parameter ranges:** lab 10 keV–2 MeV, θ 0–180°; spectrum θ ∈ {0, 45, 90, 135}° (free 0–180° at İleri); angular tab 1 keV–10 MeV.

## 3. Verification table (all run in-browser; 22/22 pass)

| Test | Expected | Source | Result |
|---|---|---|---|
| λ_C = h/(m_ec) from constants | 2.426 310 238 67 pm | CODATA 2018 | pass (< 1e-9) |
| Δλ(90°) | λ_C | analytic | pass |
| Δλ(180°) | 2λ_C = 4.852 62 pm | analytic | pass |
| Δλ independent of E (10 keV vs 2 MeV, 60°) | 0 | Compton 1923 | pass (4e-15 pm) |
| E′(180°), E = 511 keV | 170.333 keV | textbook E/3 | pass |
| Cs-137 Compton edge | 477.334 keV | Knoll; E_γ = 661.657 keV (NNDC) | pass |
| Cs-137 backscatter E′(180°) | 184.32 keV | gamma-spectroscopy textbooks | pass |
| Compton 1923, Mo Kα on graphite, 90° | 2.2 pm measured (0.022 Å) | Phys. Rev. 21, 483, p. 494 | pass, model 2.43 pm, tolerance 0.35 pm. The ~10 % difference is the 1923 experimental error. Compton himself compared 0.022 vs 0.024 Å and called it "very satisfactory". |
| Mo Kα₁ λ from NIST energy | 70.932 pm | NIST SRD 128 | pass |
| Energy conservation, T rebuilt relativistically from p_e = p − p′ | 0 | conservation law | pass (4e-15) |
| Momentum conservation, x and y components using model φ and T | 0 | conservation law | pass (2e-13) |
| cot-form φ vs atan2(p′ sin θ, p − p′ cos θ) | 0 | two independent expressions | pass |
| φ at θ → 0 | 90° | analytic limit (original gave 0°) | pass |
| σ_T = 8πr_e²/3 from constants | 6.652 458 7321e-29 m² | CODATA 2018 | pass |
| KN → Thomson at 1 eV, 120° | (r_e²/2)(1 + cos²θ) | analytic limit | pass (6e-6) |
| ∫dσ_KN/dΩ dΩ (numeric) vs closed form, 662 keV | 0.256 20 b | analytic | pass (< 1e-5) |
| σ_KN(1 MeV) | 0.2114 b | NIST XCOM, H incoherent | pass (0.09 %) |
| σ_KN(662 keV) | 0.2563 b | NIST XCOM, H incoherent | pass (0.04 %) |
| σ_KN(10 keV) vs series σ_T(1 − 2k + 26k²/5 − 133k³/10) | 6.404 67e-29 m² | Heitler, low-energy expansion | pass (5e-6) |
| Monte Carlo ⟨cos θ⟩ at 662 keV, 40 000 seeded samples | 0.3187 | numeric KN average | pass (Δ = 0.001, ~1σ) |
| β < 1 and 0 ≤ φ ≤ 90° over E and θ grid | – | kinematic consistency | pass |
| Spectrum model: shifted valence peak at 90° within ±0.15 pm of λ̄(Kα) + λ_C | – | consistency of spectrum and kinematics | pass |

## 4. Historical claims with sources

- Barkla showed X-ray polarisation (1905), and early scattering experiments supported Thomson's theory. Sources: Barkla, Phil. Trans. R. Soc. A 204, 467 (1905); Compton 1923, introduction ("supported by the early experiments of Barkla and others"). Barkla won the 1917 Nobel Prize for characteristic X-rays (nobelprize.org).
- Compton at the Cavendish 1919–20 (γ-ray scattering). His earlier "large electron" hypothesis was abandoned because the required size varied with wavelength. Sources: Compton 1923 introduction; Wikipedia biography citing the NRC fellowship; E. Henriksen, Physics Today 75(12), 44 (2022).
- Compton was appointed Wayman Crow Professor and head of physics at Washington University in St. Louis in 1920, and moved to Chicago in 1923. Sources: Henriksen 2022; Wikipedia.
- He presented the result at the APS meeting in Chicago in early December 1922 and submitted the paper on 13 December 1922. Sources: Henriksen 2022; the paper's dateline "Washington University, Saint Louis, December 13, 1922" (OCR'd copy).
- Phys. Rev. 21, 483 (May 1923): Mo Kα 0.708 Å → 0.730 Å at 90°, Δλ = 0.022 Å (exp.) vs 0.024 Å (theory); Δλ = 0.0484 sin²(θ/2) Å. Source: the paper, pp. 483 (abstract) and 494, Fig. 4.
- Debye's independent theory, Phys. Z. 24, 161 (1923). It was submitted after Compton's but printed earlier, and Debye acknowledged Compton's priority. Source: Henriksen 2022; Univ. Barcelona HFQ bibliography entry. The exact month is not stated in the UI ("1923"), because sources differ (one vs two months earlier).
- Phys. Rev. 22, 409 (Nov 1923): Mo rays scattered by graphite at 45°, 90°, 135°, compared with the primary. Each line splits into unmodified and modified lines; the modified line is less homogeneous, weaker at small angles and stronger at large ones. Source: abstract as indexed (scilit / search summary). I could not open the full text, so no numerical values from that paper are used.
- Bohr–Kramers–Slater (Feb 1924); Bothe & Geiger, Z. Phys. 32, 639 (1925; received 25 April 1925); Compton & Simon, "Directed quanta of scattered X-rays", Phys. Rev. 26, 289 (1 Sept 1925). Sources: Wikipedia "Bothe–Geiger coincidence experiment"; scilit record.
- Nobel 1927 shared with C. T. R. Wilson. Wilson's cloud chamber showed recoil electrons by the end of 1923. Sources: Henriksen 2022; Wikipedia.
- Klein & Nishina, Z. Phys. 52, 853 (1929); DuMond, Phys. Rev. 33, 643 (1 May 1929) attributes the breadth of the modified line to electron velocities in the solid. Sources: Wikipedia; Caltech authors record.
- Numbers: NIST SRD 128 Mo KL₂ = 17 374.29(29) eV and KL₃ = 17 479.372(10) eV (queried 2026-11-12). NIST XCOM hydrogen incoherent: 0.2563 b (0.662 MeV), 0.2114 b (1 MeV), 0.1466 b (2 MeV). Hubbell et al., J. Phys. Chem. Ref. Data 4, 471 (1975), Table I carbon.
- Not used: anecdotes, quotes beyond short phrases from the 1923 paper, and Duane's controversy. I could not verify its dates well enough, so it was left out.

## 5. Known limitations

- Collision view: free electron at rest (no binding, no Doppler).
- Spectrum: graphite is treated as independent C atoms (amorphous). Several things are absent: Bragg reflections of crystalline graphite (Debye–Scherrer rings), interatomic interference, absorption, multiple scattering, Kβ, and polarisation of the tube output.
- The valence Compton profile is a Gaussian (σ = 0.9 a.u.). The real graphite profile is anisotropic and non-Gaussian, J(0) ≈ 2.
- The core profile is hydrogenic with an energy-transfer cutoff, which is crude near threshold.
- Splitting S into core and valence using a Slater 1s form factor ignores exchange terms.
- Compton's slit widths are not given in his papers, so the wide-slit σ = 0.40 pm is chosen to resemble his figure.
- Compton's 1923 wavelength scale (0.708 Å for Mo Kα) differs from the modern 0.7093 Å by ~0.3 %. The model uses modern NIST values and the UI states this.
- KN is for unpolarised photons on free electrons, with no radiative corrections (≤ 0.2 % vs XCOM at 1–2 MeV).
- Event mode counts single Compton scatters only. There is no photopeak, detector resolution, or multiple scattering, so the T histogram is the ideal Compton continuum.
- Doppler mapping uses the small-shift formula δλ = 2λ sin(θ/2) p_z/(mc) rather than the full relativistic p_z(E′) relation. This is fine at 17 keV.

## 6. Core-template changes

One minimal fix in `Q4.sci` (bug): when the mantissa rounds up to 10 (e.g. 9.99996e-5 with d = 3), it printed "10,000 × 10⁻⁵". The fix adds:

```js
let p=Math.floor(Math.log10(Math.abs(v))), m=v/10**p;
if(Math.abs(+m.toFixed(d))>=10){ m/=10; p++; }
```

(`const` → `let` plus one line). Recommend merging into `sablon.html`. Everything else in the CSS and core is verbatim.

Also applied the coordinator's two template fixes (clearRect in `cv.redraw`, `details > *{box-sizing:border-box}`). Apart from the `sci` fix above, the core and CSS are now identical to the current `sablon.html`. The local `cvs()` wrapper that clears the canvas is now redundant but harmless.