PHOTON RECOIL / ANGULAR SPECTRA

Compton Angular Spectrometer

Rotate a calibrated energy detector around a scattering target. Retain individual photopeak pulse heights and estimate the incident energy and electron rest energy from an angular scan.

Free stationary electrons, one scattering, unpolarized photons and a narrow meridional slit. Conditional full-energy photopeak events with Gaussian energy resolution; no continuum, binding, efficiency or absolute rate model. Known angle and energy calibrations. Synthetic records test inference, not the historical discovery or QED.

Incoming photons travel rightward. The detector faces the target at the selected angle. Paths and sizes are schematic; energy data appear below.

CALIBRATED PULSE HEIGHTS / RETAINED EVENTS

Turn the detector. Build an energy curve.

Collimated photonPassive scattering targetRotating energy detector

A scan records the selected number of individual photopeak pulses at each of fifteen angles, from twenty through one hundred sixty degrees. These are conditional detected events, not a count-rate or cross-section measurement.

Ready. Predict, then acquire.

RAW DETECTOR RECORDS

Energy falls as the angle opens.

$\theta/\mathrm{deg},\quad E_\gamma/\mathrm{keV}$

Retained pulsesFitted meanSaved pulses

Thin gold: separate source mean, not acquired data. Every displayed point comes from a retained pulse. Dense scans can overlap.

RECORDED CENTROIDS / FIT RESIDUALS

Check the angular response.

$\theta/\mathrm{deg},\quad (\overline E-\widehat E)/s_{\overline E}$

CURRENT ANGLE / RECORDED PHOTOPEAK

Inspect the pulse-height population.

$E_\gamma/\mathrm{keV},\quad N_{\rm bin}$

This histogram rebins only the retained pulses at the current angle. Moving the detector after a scan selects another recorded population. Counts outside the displayed range remain in the export and fit.

INFERENCE / RECORDS ONLY

What the retained observations support

Retained events

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Inferred incident energy

\text{—}

Inferred electron rest energy

\text{—}

Centroid residual RMS

\text{—}

Known energy calibration and slit geometry are required. The fit searches incident energy from 450 to 850 keV and rest energy from 300 to 750 keV. Boundary fits are flagged; residual RMS is not a parameter confidence interval.

IN-MEMORY COMPARISON

Save a run to compare or restore its settings and raw events.

Measure recoil in coincidence Read the historical evidence ORTEC apparatus reference Compton 1923 paper

Start with the essentials

Focus question: A scattered photon keeps less energy.
One-sentence intuition: Keep source assumptions separate from estimates made from records.

Core mathematical model

Photon energy after recoil

E_\gamma(\theta)=\frac{E_0}{1+\frac{E_0}{m_ec^2}(1-\cos\theta)}

Angle is measured from the incoming photon, not the recoil electron. Energy and momentum conservation fix the response.

A finite angular slit

\overline E_\gamma=\frac{\int_{\theta-a}^{\theta+a}E_\gamma(\vartheta)K(\vartheta)\,d\vartheta}{\int_{\theta-a}^{\theta+a}K(\vartheta)\,d\vartheta}

The meridional slit has uniform angular transmission and negligible elevation. Relative unpolarized Klein–Nishina density supplies the weight; this is not a full azimuthal ring.

Infer two energy scales

\frac1{E_\gamma}=\frac1{E_0}+\frac{1-\cos\theta}{m_ec^2}

The zero-aperture identity explains identifiability. The actual fit uses finite-slit mean energies, not the reciprocal of noisy individual pulses. Source values are excluded.

Common difficulties

A simulation supplies its law

Typical misconceptionRecovering a source parameter independently confirms the law.

Better mental modelThese synthetic records test a measurement and inference workflow. They are not historical observations, a parameter confidence interval, or external scientific certification.

Run the experiment

01
Rotate and acquire
Scan fifteen angles; inspect individual energies and retained centroids.
What to observe: Larger scattering angles give lower photon energies. The line is a fitted mean, not a synthesized spectrum.
02
Open the slit
Save a comparison, then scan the wide-slit preset.
What to observe: Angular acceptance broadens energy populations; the estimator integrates the same calibrated acceptance.
03
Demand angular information
Acquire repeated batches at just one angle.
What to observe: A single energy centroid cannot separate incident and electron rest energies. At least five populated angles over ninety degrees are required.